Question

A researcher hypothesizes that caffeine will affect the speed with which people read. To test this, the researcher randomly assigns 8 people into one of two groups: 50mg Caffeine (n1=4) or no Caffeine (n2=4). An hour after the treatment, the 8 participants in the study are asked to read from a book for 1 minute; the researcher counts the number of words each participant finished reading. The following are the data for each group:

50mg Caffeine (group 1)

450 400 500 450

No Caffeine (group 2)

400 410 430 440

Answer the following questions as you do a t-test between independent samples

a. Find the mean and standard deviation for each of the samples above

b. Should you do a one-tail test or two-tail test? Why?

c. What is the research hypothesis?

d. What is the null hypothesis?

e. What is df1? What is df2? What is the total df for this problem?

f. Assuming that the null hypothesis is true, what is the mean of the sampling distribution of the difference between independent sample means, μ(m1-M2)?

g. Find the estimate of the standard error of the difference between independent sample means S(m1-m2)

h. Under the assumption of the null hypothesis, what is the t-score of the difference between sample means, M1-M2?

Use α-level of .05 to answer the questions below:

i. Draw the sampling distribution of the difference between independent sample means, and locate M1-M2, μ(m1-M2) on the x-axis. What is the value of μ(m1-M2 under the assumption of the null hypothesis; indicate this on the x-axis as well.

j. Given the total df for this problem, what is the critical value of t? Indicate the critical value of t (and its value) in your drawing on (i). Also, indicate what the area is in the tail beyond the critical value of t.

k. Can you reject the null hypothesis?

l. Can you accept the research hypothesis?

Answer 1