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Mathematics8
Posted Date: 30 Jan 2008 Resource Type: Articles/Knowledge Sharing Category: Conference and Symposium
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Posted By: piyush Member Level: Gold
Rating:  Points: 5
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Mathematics
1. The time of a drug to dissolve in the body of a patient is normally distributed with mean 20 minutes. This drug is then improved with the aim to dissolve in the body quickly. The improved drug is then administered to 15 patients and the time (in minutes) to dissolve in their body were found to be 12, 8, 13, 7, 9, 5, 13, 15, 19, 23, 17, 13, 12, 24, 15. Test at 5% level of significance that on the average the improved drug takes less time to dissolve in the body. Also construct 95% confidence interval for the mean time to dissolve for the improved drug.
2. The following data represent the number of organisms found in 50 water samples collected randomly from a pound:
No. of organisms: 0 1 2 3 4 and above
No. of samples : 15 20 10 4 1
Fit an appropriate distribution to these data and then apply chi-square test of goodness of fit at 5% level.
3. A breast cancer research team collected the following data on tumor size:
Type of tumor sample size sample mean sample standard deviation
A 12 3.45 1.55
B 10 2.35 1.95
Test at 5% confidence level that the mean size of both types of tumors are same assuming the normality with equal population variances.
4. Research has suggested a high rate of alcoholism among patients with primary unipolar depression. An investigation by a researcher further explores this possible relationship. In 220individuals with primary unipolar major depression, he found that alcoholism was present in 95. Of 300 control individuals, alcoholism was present in 90. Do these data provide sufficient evidence to conclude at 5% level that alcoholism is more likely to be present in families with unipolar depression? Also construct 95% confidence interval for the difference of population proportions of alcoholics among depressed and normal families.
Department of Mathematics
JUIT, Waknaghat
MA 104 TS9
Name: Roll No.: Date:
1. The time of a drug to dissolve in the body of a patient is normally distributed with mean 20 minutes. This drug is then improved with the aim to dissolve in the body quickly. The improved drug is then administered to 15 patients and the time (in minutes) to dissolve in their body were found to be 12, 8, 13, 7, 9, 5, 13, 15, 19, 23, 17, 13, 12, 24, 15. Test at 5% level of significance that on the average the improved drug takes less time to dissolve in the body. Also construct 95% confidence interval for the mean time to dissolve for the improved drug.
2. The following data represent the number of organisms found in 50 water samples collected randomly from a pound:
No. of organisms: 0 1 2 3 4 and above
No. of samples : 15 20 10 4 1
Fit an appropriate distribution to these data and then apply chi-square test of goodness of fit at 5% level.
3. A breast cancer research team collected the following data on tumor size:
Type of tumor sample size sample mean sample standard deviation
A 12 3.45 1.55
B 10 2.35 1.95
Test at 5% confidence level that the mean size of both types of tumors are same assuming the normality with equal population variances.
4. Research has suggested a high rate of alcoholism among patients with primary unipolar depression. An investigation by a researcher further explores this possible relationship. In 220individuals with primary unipolar major depression, he found that alcoholism was present in 95. Of 300 control individuals, alcoholism was present in 90. Do these data provide sufficient evidence to conclude at 5% level that alcoholism is more likely to be present in families with unipolar depression? Also construct 95% confidence interval for the difference of population proportions of alcoholics among depressed and normal families.
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Responses
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| Author: Vidya 23 May 2008 | Member Level: Diamond Points : 2 | gud
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