A scientist was worried that the quality of the blood they were using for ongoing experiments was degrading with longer storage times. They obtained blood from 40 volunteers and divided each blood sample up into four parts. They then measured the percent of CD4 and CD8 cells that were expressing CD127 from each sample at 4 hours, 24 hours, 48 hours and 72 hours.

1. Using the function t.test(), Construct a 95% confidence interval for the mean %CD127 at 4 hours. Describe the set of plausible values for the true mean.

2. Test the hypothesis that the true mean %CD127 is 40 in this population. What is the p-value? Write a one-sentence conclusion from the test, based on a two-sided alpha of .05.

3. Looking back at your answer to part (a), how could you have answered (b) without doing another test?

Now create a new variable showing the change since 4 hours to 72 hours.

1. Make a histogram of the change variable, and get the 95% CI for mu. "No change" would be equivalent to a mean change of 0. Does the Confidence interval include 0? What can you say about change from 4 hours from this confidence interval?

2. Do a t-test as to whether the mean change at 72 hours is significantly different than 0. What is the p-value? Write a one-sentence conclusion from the test, based on a two-sided alpha of .05.

3. Looking back at your answer to part (d), how could you have answered (e) without doing a test?