Question

A clinical trial was conducted to test the effectiveness of the drug Zopiclone for treating insomnia in older subjects. Before treatment with Zopiclone, 16 subjects had a mean wake time of 102.8 minutes. After treatment with Zopiclone, the 16 subjects had a mean wake time of 98.9 minutes and a standard deviation of 42.3 minutes. Show Work:

1. Assume that the 16 samples values appear to be from a normally distributed population, and test the claim that after treatment with Zopiclone, subjects have a mean wake time of less than 102.8 minutes.

2. Test the claim by constructing an appropriate confidence interval.

3. Test the claim by constructing an appropriate confidence interval.    
4. What are the null and alternative hypotheses?
5. What is the value of α= significance level?
6. Is the test two-tailed, left-tailed or right-tailed?
7. What is the test statistic and what is its distribution?
8. What is the value of the test statistic?
9. What is the P-value?
10. What is (are) the critical value(s)?
11. How would you state a conclusion that addresses the original claim?

Answer 1

-------------------------------------------------

Since population standard deviation is unknown so t dstribution will be used.

-----------------------------------------------

Conclusion: There is no evidence to support the claim that after treatment with Zopiclone, subjects have a mean wake time of less than 102.8 minutes.

-----------------------------------------

Confidence interval:

Here test s left tailed so we need one side 95% confidence interval. So,

Hence, the required confidence interval is (80.36, infinity).

Conclusion: Since confidence interval contains 102.8 so we fail to reject the null hypothesis on the basis of confidence interval. There is no evidence to support the claim that after treatment with Zopiclone, subjects have a mean wake time of less than 102.8 minutes.