Question

The ages of a group of 124 randomly selected adult females have a standard deviation of 17.6 years. Assume that the ages of female statistics students have less variation than ages of females in the general​ population, so let sigmaσequals=17.6 years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics​ students? Assume that we want 99​% confidence that the sample mean is within​ one-half year of the population mean. Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general​ population?

The required sample size is____

2) In a test of the effectiveness of garlic for lowering​ cholesterol, 44 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes ​(beforeminus−​after) in their levels of LDL cholesterol​ (in mg/dL) have a mean of 3.8 and a standard deviation of 17.3 Construct a 99​% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment.

What is the confidence interval estimate of the population mean

___​mg/dL<u<____mg/dL

​(Round to two decimal places as​ needed.)

Answer 1

1)

Margin of error, E= +/- 1.5 year

At =0.01, the critical value, = 2.58

Sample size, n=

So, the required sample size is 916.

2) Mean of the changes(before-after), = 3.8

Standard deviation, = 17.3

Sample size, n= 44

At =0.01 and df = 44-1 = 43,the critical value, = 2.70

99% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment