Question

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. After​ treatment, the 20 subjects had a sample mean wake time of 93.8 minutes and a sample standard deviation of 21.6 minutes. Assume that the sample values appear to be from a normally distributed population. Construct a 95% confidence interval estimate of the mean wake time for a population with drug treatments.

a)     Verify that the conditions are met. Show your work. (2 pts)

b)     Construct the confidence interval. Round to one decimal place. Show your work. (16 pts)

c)      Write the correct interpretation of the confidence interval. (2 pts)

Answer 1

a) The values provided in the questions are as follows

Mean of the sample = = 93.8

Standard deviation of the sample = S = 21.6

Sample size = n = 20

Here population standard deviation is not known and also sample size is 20 which is less than 30

So we used t test instead of given distribution are normal distribution.

b)The formula of 95% confidence interval of population mean is as

We find critical value of t using following command in Excel

=TINV(probability, degrees of freedom)

For two tailed test we distribute the level of significance 0.05 into two eqaul parts that is = 0.05/2 = 0.025

Using TINV(0.025, 19) command in Excel then press Enter

Critical value of t with 0.05 significant level at 19 degrees of freedom = 2.43

The range confidence interval of population mean are 82.1 to 105.5

c) The interpretation of the confidence interval.

The 95% confidence interval estimate of the mean wake time for

a population with drug treatments are lies between 82.1 to 105.5