Question

A psychologist believes that students' test scores will be affected if they have too much caffeine before taking an exam. To examine this, she has a sample of n = 4 students drink five cups of coffee before taking an exam. A week later the same n = 4 students did not drink any coffee before taking a similar exam. Do a related samples t-test using α = .01.

Student Test 1(Caffeine) Test 2(No Caffeine)

Abe 70 70

Bill 72 75

Charlie 75 80

Doug 90 96

a. is this a one-tailed test or a two-tailed test?

b. What is the research hypothesis?

c. What is the null hypothesis?

d. Calculate the degrees of freedom for this problem

e. What is the critical value of α=.01

f. Calculate the mean of the distribution of sample means

g. Calculate the estimate of the standard error of the mean

h. Calculate the t-score of the sample mean

i. Sketch the distribution of sample means and indicate where the sample means is, where the critical value of t is located

j. Can you reject the null hypothesis?

k. Can you accept the research hypothesis?

Answer 1

students	coffee	no coffee	difference (no coffee- coffee)
Abe	70	70	0
Bill	72	75	3
Charlie	75	80	5
Doug	90	96	6

,

a) This is a Two tail test

b) Research hypothesis,

c) Null hypothesis ,

e) degree of freedom= n-1 = 4-1=3

f) Critical value,

g) Standard error of mean,   =

h) t-score. = = 2.6455

i) graph will be like   

j) since test statistics value lie in the critical region so we will accept the null hypothesis

h) so, we cannot accept the research hypothesis.