Using the data set posted just above, answer the following questions.

Using the data set posted just above, answer the following questions.
1. For the moment, assume these data came from 2 independent groups. Group 1 represents the control group in the study which was given a placebo. Group 2 represents a treatment group which was given a medication suspected to increase reaction time. The response time column gives the reaction times for both groups measured in centiseconds (cs). We are interested in testing the hypothesis of does the drug has an effect on reaction time or not.
a. State the null and alternative hypothesis
b. Calculate the pool standard deviation
c. Calculate the t-score
d. Give the critical value of the t-distribution and p-value for this test
e. Do you reject or fail to reject the null?
2. Now suppose I tell you Group 1 is the pre-medicated measurement and Group 2 is the post-test measurement for 25 people. The first value in the list for Group 1 and Group 2 is the first person, the second value is the second person and so on. Given this, we are still interested in if the drug effects reaction time or not.
a. State the null and alternative hypothesis
b. Calculate the pool standard deviation
c. Calculate the t-score
d. Give the critical value of the t-distribution and p-value for this test
e. Do you reject or fail to reject the null?
3. Below is an example output given to you by a biostatistician. This is the result of an analysis done on a previous study. Based only on this output, which test (independent or paired t-test) do you think was done for this study? Be clear and explain using the output why you think one way or the other.
Mean 95% CL Mean Std Dev 95% CL Std Dev
-19.2329 -22.3007 -16.1651 6.5550 4.9850 9.5740

DF t Value Pr > |t|
19 -13.12 <.0001