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· Answer all questions. · Marks are indicated against each question. |
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A die is
loaded so that the probability of getting face x is proportional to
x. Then the probability of getting less than or equal to three is:
(2
marks) |
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If the
probability that A will be alive for 20 years is 0.7 and the
probability that B will be alive for 20 years is 0.5, then what is
the probability that both will be alive for 20
years?
(1
mark) |
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A ball is
drawn at random from a box containing 6 red balls, 4 white balls and 5
blue balls. What is the probability that the ball drawn is ‘not
red’?
(2
marks) |
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Two dice are thrown simultaneously. The probability that the sum of the numbers on them is less than or equal to 5 is
(2
marks) |
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In a
simultaneous tossing of two unbiased coins, the probability of having
atleast one tail is
(1
mark) |
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A and B are
two independent events such that P(A) = 0.3, P(B) = k and P(A or B) = 0.8,
then the value of k is equal to
(1
mark) |
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Which of the following is/are the conditions for applying the Bayes’ theorem for computing posterior probabilities of certain events?
(1
mark) |
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If events A
and B are mutually exclusive then which of the following is
true?
(1
mark) |
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Which of the
following best describes the expected value of a discrete random
variable?
(1
mark) |
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The expected
value of the number of successes of a binomial distribution is equal to
(1
mark) |
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Which of the
following statements is/are false with regard to a normal
distribution? I. It is
a continuous distribution. II. It is a
multimodal. III. It is an asymmetrical
distribution. IV. The mean, median and
mode are equal.
(1
mark) |
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The
probability distributions of independent random variables X and Y, are given
below:
If a random variable Z, is defined as: Z = 4X +
5Y What is the expected value of the
random variable Z?
(2
marks) |
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The persons A and B together tosses a coin, then the
probability of A’s success is 2/3. The standard deviation of the number of
success in a binomial distribution is given
by Find the probability of obtaining exactly 9 successes?
(2
marks) |
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Sanjunath is an incharge of the music
section of a large departmental store. He has noticed that a customer who
is just browsing will buy something is 0.3. Suppose that 15 customers
browse in the music section in an hour. What is the probability that not more
than four browsing customers will buy something during the specified
hour?
(2
marks) |
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Which of the
following is/are the example(s) of Poisson
distribution? I. The
number of deaths in a city due to suicides. II. The number
of defective items in a box of 100 items. III. The number of plane
accidents per week.
(1
mark) |
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Which of the
following is not a characteristic of Bernoulli
process?
(1
mark) |
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If
(1
mark) |
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Which of the
following is/are not true? I. F-distribution extends along
abscissa from 0 to II. F-distribution curve wholly lies
in the first quadrant. III. Shape of the curve
depends on the sample sizes n1 and
n2.
(1
mark) |
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The
probability of success changes from trial to trial in
(1
mark) |
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If there are
infinite number of possible number of outcomes, the probability of any one
outcome is
(1
mark) |
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The sampling
distribution of the mean is a distribution of
(1
mark) |
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Which of the
following is false with regard
to standard error of mean?
(1
mark) |
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A sample of
size 96 has been taken from a population and the estimated standard error
of proportion is found to be 0.05. What is the sample
proportion?
(2
marks) |
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For which of
the following distributions the z-values and the observed values are
same?
(1
mark) |
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In random
sampling, we can describe mathematically, the objectiveness of our
estimates. This is because I. We always know the chance, that any population element will be included in the sample. II. Every sample always has an equal chance of being selected. III. All the samples are of same size and can be counted.
(1
mark) |
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A statistic
which comes very close to the value of the population parameter as the
sample size increases is said to be
(1
mark) |
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Which of the
following statements is true?
(1
mark) |
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In making
estimates of population parameters using sample statistics, efficiency
refers to the
(1
mark) |
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The variance
of the sampling distribution of mean is
(1
mark) |
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Which of the
following is/are not required
for calculating the test statistic for testing a hypothesis about a
population variance?
(1
mark) |
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In order to
find out the critical value for a hypothesis test on the variance of a
population which of the following need not be
known? I.
Sample variance. II. Sample
size. III. Significance
level. IV. Type of test (one
tailed or two tailed).
(1
mark) |
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If a
hypothesis is tested at a significance level of 10% then it means
that
(1
mark) |
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Which of the
following statements is false?
(1
mark) |
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If we reject
H0:
(1
mark) |
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The ball
bearings in a large consignment have a mean weight of 142.3 grams and a
standard deviation of 8.5 grams. A random sample of 100 ball bearings is
taken from the consignment. What is the probability that the sample mean
lies between 140.61 and 141.75 grams?
(2
marks) |
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The central
limit theorem
(1
mark) |
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The 75 members of branch executives were sampled from all other executives in a specific industry and were classified into three age groups, labeled A, B, and C. It is believed that there is an equal likelihood that any branch executive selected at random will fall in any of the three age groups. There were 28 branch executives in group A, 22 in group B and 25 in group C. The belief is to be tested at a significance level of 0.05, using a suitable technique. What is the value of the test statistic?
(3
marks) |
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For a sample
randomly collected from a population, the following details are
available:
(2
marks) |
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In the test involving ANOVA the F-statistic is calculated on the basis of
(1
mark) |
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When the
chi-square test is used as a test of independence, the number of degrees
of freedom is determined by
(1
mark) |
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A 95%
confidence interval for the proportion of male drunken drivers in a given
state is to be constructed and must be accurate to within
(2
marks) |
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Which of the
following is/are the method(s)
of finding the correlation between two variables?
I.
Method of least squares. II. Spearman’s
rank correlation coefficient. III. Scatter
diagram.
(1
mark) |
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Capital
Finance Company Ltd. is a non-banking finance company. In the recent years
there have been variations in the demand for loans as well as in the rate
of interest. The general manager of the company wants to know whether the
variations in the amount of advances explain the variations in the net
profit of the company. The following data pertain to the
operations of the company in the recent years:
What is the
coefficient of correlation between the net profit and the amount of
advances?
(3
marks) |
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A sample of
paired observations of two random variables X and Y is given
below:
What is the
covariance between X and Y?
(2
marks) |
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Two simple
regression relationships have been developed between variables X and Y;
and between variables W and Y. In both the relationships variable Y is the
dependent variable. The coefficient of correlation between variables X and
Y is 0.85 and the coefficient of correlation between variables W and Y is
– 0.92. Which of the following statements
is/are correct?
(2
marks) |
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Which of the
following is true when the slope of a regression line is
negative?
(1
mark) |
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In the
linear regression model, the residuals are assumed
to
(1
mark) |
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The
following details are available with regard to a simple regression
relationship: Total sum of
squares = 16730 Error sum of
squares = 1630 What
percentage of the variations in the dependent variable is explained by the
regression relationship?
(2
marks) |
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Prestige Industries Ltd. (PIL) has a sales force
consisting of 150 salespersons having various number of years of sales
experience. The sales manager of the company wants to establish a
relationship between the number of years of experience and annual sales.
The following data are collected by him from a random sample of 10
salespersons of the company:
A simple regression relationship has to
be developed for estimating the annual sales on the basis of the number of
years of experience of the salesperson. Which of the
following is the estimated amount of annual sales if a salesperson has 10
years of experience?
(3
marks) |
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A simple
regression relationship was developed between the variables X and Y, with
X as the independent variable. The estimated value of Y when X = 2, is
7.0; and the estimated value of Y when X = 8, is 11.8. What is the value
of the coefficient of X?
(2
marks) |
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A simple
regression relationship was developed between two variables X and Y, where
X is the independent variable with slope 5 and intercept as 3. The
following information is given below: S Y2 = 780
SXY = 452
SY = 72 n =
8 Find the coefficient of
determination?
(2
marks) |
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Pyramid
Networks Ltd. manufactures and sells network access software products. Its
sales have been increasing in the recent years. The company is planning to
expand its work force in response to the increasing trend shown by the
sales of its products. The future manpower requirement is expected to be
dependent on the level of future sales. The company requires an estimate
for the sales in the year 2007. The following data are
collected:
The sales
for the year 2007, estimated on the basis of a linear trend equation,
is
(2
marks) |
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If the
regression equation is not a perfect estimator of the dependent variable
then which of the following will be true? I. The
standard error of estimate is not zero. II. The
coefficient of determination is not one. III. The data points do not
lie on the regression line. IV. Error sum of squares is
equal to zero.
(1
mark) |
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Which one of
the following is not true with regard to simple linear
regression?
(1
mark) |
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Which
criterion of decision-making is not applicable when the decision
maker has insufficient information to assign any probabilities of
occurrence to the various states of nature?
(1
mark) |
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The maximum
criterion for decision making suggests that the alternative with the
(1
mark) |
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Which of the
following is a tool for making decisions involving many alternatives and
different states of nature which can be specified in terms of
probabilities?
(1
mark) |
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The expected value of perfect
information is equal to the difference between I. The
highest gain possible under certain conditions. II. The least
gain possible under certain conditions. III. The highest expected
profit under uncertain conditions. IV. The least expected
profit under uncertain conditions. V. The
expected profit with perfect information. VI. The highest expected
profit without perfect information. VII. The least expected profit
without perfect information.
(1
mark) |
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In marginal
analysis the minimum required probability of selling an additional unit,
that justifies stocking of that additional unit,
(1
mark) |
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Which of the
following is not true for random variables?
(1
mark) |
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Which of the
following can be defined as a systematic and objective process of
gathering, recording and analyzing data to guide business
decision-making?
(1
mark) |
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If the
sampling frame is arranged in ascending or descending order, the sample
selected by the systematic sampling method will be affected
by
(1
mark) |
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Which of the
following is the measure of how close an estimate is expected to be, to
the true value of the parameter?
(1
mark) |
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Which of the following is/are the preliminary decision(s) of a questionnaire design? I. Required information. II. Target respondents. III. Interviewing technique.
(1
mark) |
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The statistical difference in results between a survey that includes only those who responded and a perfect survey that also include those who failed to respond is
(1
mark) |
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Which of the
following does not come under
the category of asymmetrical relationship?
(1
mark) |
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The scale
which helps segregate data into categories that are mutually exclusive and
collectively exhaustive is
(1
mark) |
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For
instance, if the researcher is conducting intercept interviews in public
places then the researcher may not respond as properly as they would if
they were interviewed in their homes, this type of research error comes
under
(1
mark) |
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Which
graphical representation is best suitable for the changes/trends in the
demand for a product?
(1 mark) |
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Which of the
following is undertaken to verify the data and check for any potential
errors or for any inconsistencies?
(1 mark) |
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How would
you print a bar chart that you have produced in SPSS?
(1 mark) |
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To generate
the Spearman's rho test, which set of instructions should we follow in
SPSS?
(1 mark) |
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In which
sub-dialog box can the Chi-Square test be found?
(2 marks) |
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When
cross-tabulating two variables it is conventional to:
(1 mark) |
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What should
the business researcher do if their multi-strategy approach produces
inconsistent results?
(2 marks) |
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What is/are
the advantage(s) of using SPSS over calculating statistics by hand?
I. This
is how most quantitative data analysis is done in 'real research'
now-a-days. II. It reduces
the chance of making errors in your calculations. III. It equips you with a
useful transferable skill.
(1 mark) |
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.
. 
= a + b1X1 +
b2X2, where X1 and X2 are two
independent variables, then the problem of multicollinearity will arise
when the
.
= 10
10
= 1840
0.08 of the point estimate. A preliminary sample
provides an initial estimate of the proportion as 0.09. The smallest
sample size that will provide the desired accuracy
isSuggested
Answers
Quantitative Methods-II (MB152): January
2007
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Answer : (b) Reason : There are six faces in
a die and they are named as 1, 2, 3, 4, 5 and 6. So, the corresponding
probability would be 1k, 2k, 3k, 4k, 5k and 6k respectively. Since one of
the face must appear the sum of all these probabilities should be one i.e.
k + 2k + 3k + 4k + 5k + 6k = 21k = 1 or k
=
The probability of getting less than or equal to three is 1k +2k +
3k = 6k = |
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Answer : (a) Reason : Since the events A and
B are independent then, the probability of A and B is = |
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Answer : (d) Reason : The total number of balls other than red are 9.
So a ball can be drawn from 9 non red balls in
And the ball is drawn from total of 15 balls in
P(not Red) = |
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Answer : (d) Reason : Total number of possible event = 36. The set of favorable event is E = {x, y}, such that (x + y) £ 5, E = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1)} Thus total number of favorable event = 10. Therefore required
probability = P(E) = |
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Answer : (b) Reason : Here, the sample space may be drawn as (HH, HT, TH and TT). The number of cases that are favorable is given by 3 while the total number of possible outcomes is 4. Hence, the required probability is = 0.75. |
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Answer : (d) Reason : Here, P(A) = 0.3 and P(B) = k while, P(A or B) = P(A) + P(B) – P(A).P(B) (as the events are independent) = 0.8 Therefore, 0.3 + k – 0.3´k = 0.8 or, 0.7´k = 0.5 or, k = 5/7. |
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Answer : (e) Reason : The events for which the Bayes’ theorem may be applied for computing posterior probabilities must be mutually exclusive and collectively exhaustive. |
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Answer : (a) Reason : Two mutually exclusive events, A and B, cannot occur together. \ P(A and B) = 0. None of the other alternatives are implied by the definitions of mutually exclusive events. |
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Answer : (c) Reason : a. The expected value of a discrete random variable is not a geometric average of the outcomes of the variable. b. The expected value of a discrete random variable is not a simple average of the outcomes of the variable. c. The expected value of a discrete random variable is a weighted average of the outcomes of the variable. d. The expected value of a discrete random variable is not the outcome, which has the highest frequency. e. The expected value of a discrete random variable is not the highest probability of occurrence in the distribution of the random variable |
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Answer : (e) Reason : The mean (expected value) of the number of successes in a binomial distribution is equal to the product of the number of trials and probability of success in any trial. |
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Answer : (c) Reason : Normal distribution is a continuous distribution. It is unimodal and symmetrical. The mean, median and mode are equal. |
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Answer : (e) Reason : E(Z) = E(4X + 5Y) = 4E(X) + 5E(Y)
= = 74 + 74 = 148 |
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Answer : (d) Reason : Probability of success p = 2/3. Then q = 1– p = 1/3. To find the value of n, put the values of p and q in variance. i.e. variance = npq
3.33 = n = 15
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Answer : (e) Reason : The total number of
customers browsing the music section is 15. The probability that a
customer will buy something is 0.3. This follows a Binomial Distribution
with n = 15, p = 0.3 and q = 0.7. For exactly r successes out
of n trials is The probability that no more than four browsing customers will buy something during a specified hour = P(0) + P(1) + P(2)+ P(3) + P(4) = = 0.51549. |
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Answer : (e) Reason : The constant probability p of success for each trial is very small and the number of trials is indefinitely large. So, all the given examples follows Poisson distribution. |
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Answer : (d) Reason : Alternative (a), (b),(c) and (e) are the characteristics of a Bernoulli process. The probability of two outcomes not necessarily should be same. |
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Answer : (c) Reason : As the degree of correlation between the two independent variables increases, the problem of multicollinearity arises. Other options are wrong. |
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Answer : (c) Reason : Shape of the curve of F-distribution depends on the degrees of freedom n1 and n2 But not on the sample sizes. |
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Answer : (c) Reason : The probability of success changes from trial to trial in Hypergeometric distribution. |
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Answer : (b) Reason : If there are infinite number of possible number of outcomes, the probability of any one outcome is zero. |
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Answer : (d) Reason : a. The sampling distribution of mean is not a distribution of means of individual populations. b. The sampling distribution of mean is not a distribution of observations within a population c. The sampling distribution of mean is not a distribution of observations within a sample. d. The sampling distribution of mean is a distribution of means of all possible samples of a specific size taken from a population. e. The sampling distribution of mean is not a distribution of means of samples of a specific size taken from different population |
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Answer : (e) Reason : a. The standard error of mean is less than the population standard deviation(σ) because it is equal to σ/√n. b. From above we can see that it will decrease as the sample size increases. c. The standard error is a measure of the variability of the mean across various samples of the same size taken from the population. d. It is the standard deviation of the distribution of means of all possible samples of a specific size that can be taken from the population. e. From above we can see that the standard error of mean is not the standard deviation of the sample. |
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Answer : (d) Reason : Or \
or or
\
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Answer : (b) Reason : The z-values and the observed values are same for standard normal distributions. |
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Answer : (d) Reason : In random sampling, every sample has an equal chance of being selected. We always know the chance, that any problem element will be included in the sample. |
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Answer : (b) Reason : A statistic which comes very close to the value of the population parameter as the sample size increases is said to be a consistent estimator. |
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Answer : (d) Reason : While dealing with census the chances of errors are very less due to a large size. So the option (d) is true and (a), (b), (c) and (e) are false |
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Answer : (a) Reason : In making estimates of population parameters using sample statistics, efficiency refers to the size of the standard error of the sample statistics |
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Answer : (b) Reason : The variance of the sampling distribution of mean is less than the variance of the underlying population if the sample size is more than one. |
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Answer : (b) Reason : For calculating the test statistic for a test of population variance the population size is not required. |
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Answer : (a) Reason : Sample variance need not be known. All others are required. |
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Answer : (a) Reason : a. If a hypothesis is tested at a 10% significance level then, it means that there is a 10% probability that the null hypothesis will be rejected though it is true. b, c, d & e are incorrect interpretations of the significance level |
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Answer : (c) Reason : The purpose of hypothesis testing is to make a judgment about the difference between the sample statistic and the hypothesized population parameter. The purpose of hypothesis testing is not to test the correctness of the sample statistics. Alternative (c) is false. Alternatives (a), (b) (d) and (e) are true. |
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Answer : (b) Reason : If we reject
H0:m = 10 in
favor of H1:m |
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Answer : (d) Reason : From the given values
we have z = (x –
Z = (140.61–142.3)/ 8.5 = – 0.198 z = (141.75 – 142.3)/ 8.5= – 0.064. (The corresponding value of z-score of 0.064 = 0.0239) Thus, P(141.75< z < 142.3) = 0.0239. Hence P(140.61< z < 141.75) = 0.0753 – 0.0239 = 0.0514 |
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Answer : (c) Reason : The central limit theorem permits us to use sample statistics to make inferences about population parameters. |
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Answer : (d) Reason
: The appropriate
test is a chi-square test of goodness of fit. Since there is an equal
likelihood for any account executive to be in any of the three age groups,
the probability of observing any of the age groups is Hence the expected frequencies for the three age groups will be as follows:
The observed frequencies are :
The test statistic is the chi-square statistic, which is calculated below :
|
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Answer : (a) Reason : Estimated standard
error of mean = Sample
standard deviation,
\
s = \
Estimated standard error of mean = |
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Answer : (e) Reason : The F statistic is calculated on the basis of two estimates of the population variance viz., The estimated population variance based on the variance among the sample means and the estimated population variance based on the variance within the samples. |
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Answer : (e) Reason : a. This is a wrong answer. The number of degrees of freedom does not depend on the sample size. b. This is the wrong answer. The number of degrees of freedom does not depend on the ratio of sample size and the population. c. This is the wrong answer. The number of degrees of freedom does not depend on the number of rows in the contingency table only. d. This is the wrong answer. The number of degrees of freedom does not depend on the number of columns in the contingency table only. e. This is the right answer. When the chi-square distribution is used as a test of independence, the number of degrees of freedom is related to both the number of rows and the number of columns in the contingency table. |
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Answer : (d) Reason :
\The sample size should be at least 50 (we cannot round off 49.16 to the lower value because that will reduce the accuracy). |
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Answer : (e) Reason : The important methods to find the correlation between the variables are scatter diagram, Karl Pearson’s coefficient of correlation, Spearman’s rank correlation coefficient and method of least squares. |
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Answer : (a) Reason : Let the following notations be used: X : Amount of advances (Rs. in crores) Y : Net profit (Rs. in lakhs) Coefficient of correlation is given by:
r
=
\ r
= The coefficient of correlation between the net profit and the amount of advances is r = 0.9182. |
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Answer : (c) Reason
: Cov (X,Y) =
\
Cov (X,Y) = |
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Answer : (e) Reason : Coefficient of correlation between X and Y = 0.85 \ Explained variation in Y = 0.852 = 0.7225 Unexplained variation in Y = 1–0.852 = 0.2775 Coefficient of correlation between Y and W = –0.92 \ Explained variation in Y = (–0.92)2 = 0.8464 Unexplained variation in Y = 1–(–0.92)2 = 0.1536 Hence both (c) and (d) are correct. |
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Answer : (c) Reason : When the slope of a regression line is negative the dependent variable decreases as the independent variable increases. Hence increases in the independent variable can be associated with decreases in the dependent variable and vice versa. Hence, the correlation between the dependent and the independent variables is negative. |
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Answer : (b) Reason : In the linear model, the residuals are assumed to have a normal distribution with a mean of zero. |
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Answer : (d) Reason : Proportion of variations in the dependent variable explained by the regression relationship
= |
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Answer : (d) Reason : Let the following notations be used: X : Number of years of experience Y : Annual sales
SX = 80 SY = 1060 n = 10 SXY = 9048 SX2 = 782
\
b =
=
a =
\
The regression relationship is : For number of years of experience (X) = 10,
Annual sales estimated
\ For 10 years of experience the estimated annual sales will be Rs.1,14,000. |
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Answer : (a) Reason
: Given: 7 = a + b (2) (For X=2) Or 7 = a + 2 b………………….(A) 11.8 = a + b (8) (For X=8) Or 11.8 = a + 8b……………….(B)
\b
= |
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Answer : (b) Reason
: Coefficient of
determination, R2 =
\
Coefficient of determination, R2 =
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Answer : (d) Reason : Let the following notations be used: X : Year x : Coded value for year Y : Sales
b
=
a = \ The linear trend equation is
The estimated sales for the year 2007: X = 2007 \ x = (2007–2003.5) ´ 2 = 7 Estimated sales for the year 2007 = 96.67 + 12.43 ´ 7 = Rs.183.68 lakhs. |
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Answer : (d) Reason :
If the regression equation is not a perfect estimator of the
dependent variable then Therefore options (I), (II) and (III) are true. So the option (d) is correct. |
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Answer : (b) Reason : The relationship between the independent and dependent variables does not imply cause and effect. So the option (b) is true. |
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Answer : (e) Reason : When the decision maker has insufficient information to assign any probabilities of occurrence to the various states of nature expected value criterion will not be applicable. |
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Answer : (b) Reason : Under maximin criterion, the decision maker first identifies the lowest profit associated with each decision alternative and then chooses that alternative which is the maximum of the above minimum profits. |
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Answer : (b) Reason : Decision tree analysis is a tool for making decisions involving many alternatives and different states of nature which can be specified in terms of probabilities. |
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Answer : (c) Reason : The expected value of perfect information is equal to the difference between the expected profit with perfect information and highest expected profit without perfect information. |
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Answer : (c) Reason : In marginal analysis minimum required probability of selling an additional unit decreases if Marginal Profit increases. |
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Answer : (c) Reason : Statements (a), (b), (d) and (e) are true; Statement (c) is false. |
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Answer : (b) Reason : Business research can be defined as a systematic and objective process of gathering, recording and analyzing data to guide business decision-making. |
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Answer : (a) Reason : If the sampling frame is arranged in an order ascending or descending, of some attribute of the first sample element affects the result of the study. |
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Answer : (c) Reason : Precision is a measure of how close an estimate is expected to be, to the true value of a parameter. It is a measure of similarity and is expressed in terms of imprecision and related to the standard error of the estimate. |
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Answer : (e) Reason : All these are the preliminary decisions that are to be covered under a questionnaire design. So the option (e) is correct. |
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Answer : (b) Reason : The statistical difference in results between a survey that includes only those who responded and a perfect survey that also include those who failed to respond is known as non-response error. |
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Answer : (c) Reason : All other options other than (c) come under the category of asymmetrical relationships. So, option (c) is correct. |
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Answer : (b) Reason : The scale which helps
segregate data into categories that are mutually exclusive and
collectively exhaustive is nominal scale. |
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Answer : (c) Reason : The factors such as location of the interview also plays a crucial part. For instance, if the researcher is conducting intercept interviews in public places then the researcher may not respond as properly as they would if they were interviewed in their homes, this type of research error comes under situational errors. |
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Answer : (a) Reason : Bar charts can be used to represent changes or trends in the demand for a product. |
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Answer : (c) Reason : Editing is undertaken to verify the data and check for any potential errors or for any inconsistencies. It is done to remove errors that may have cropped up during the interview such as recording the answers under the wrong columns of a questionnaire. |
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Answer : (a) Reason : a.
In
Output Viewer, click file → Print, select the bar chart and click
ok. This is a straightforward way of printing your bar chart as a piece of output from SPSS. If you do not specify which things you want to print from the output summary box on the left of the screen, SPSS will print all of the graphs and tables in the Output Viewer |
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Answer : (d) Reason : Analyze → Correlate → Bivariate → [select
variables] → Spearman → ok. This set of instructions opens up the 'Bivariate Correlations' dialog box and allows you to generate a coefficient to show the strength of a relationship between two variables. |
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Answer : (b) Reason : Crosstabs: Statistics. To generate a |
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Answer : (c) Reason : Represent the dependent variable in rows and the independent variable in columns. It is conventional to represent an inferred relationship between two variables in this way because it makes tables easier to read. Similarly, when producing a bar chart or scatter plot, you should assign the Indpt.Var to the x axis (to produce columns) and the Dep.Var to the y axis (to produce horizontal readings). |
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Answer : (b) Reason : Treat one set of results as definitive. Unfortunately, if the selection of one set of data over another is entirely arbitrary, this is not an ideal approach to overcoming the difficulty of contradiction within a research project that has adopted a multi-strategy approach. Instead, researchers may wish to either explore reasons for the contrasting findings, or establish a clearly reasoned argument for the selection of one type of data as definitive. |
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Answer : (e) Reason : Option (e) is correct. In recent, most quantitative data analysts use SPSS or an equivalent statistical software package. Such tools are widely regarded as a useful transferable skill being much faster and more efficient than mental arithmetic, as they can generate huge volumes of complex statistical data with out any errors within seconds. |
. 
.
ways.
ways.
.
)/
.
)
)
(X – 
= 4
= 23
= 74.00
= 74 + 4(10) = 114 (Rs in’000s)
= 0.80.
