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= 15 students drink five cups of coffee before taking an exam. She uses an exam that has a population mean of μ=72 and a population standard deviation of σ = 3. The mean test score for the sample of 15 students who drank five cups of coffee before taking the exam was M = 69. Do a t-test using α = .01.

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 standard error of 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

Ans:

a)One tailed

b)

H, :μ< 72

c)

Η :μ = 72

d)degrees of freedom=15-1=14

e)critical value=-2.624

f) mean of the distribution of sample means=72

g)standard error of mean=3/sqrt(15)=0.775

h)

t=(69-72)/(3/SQRT(15))

t=-3.87

j)Yes ,t score is less than critical value,so reject H₀.

k)Yes