Question

A researcher conducted a paired sample t-test to determine if advertisements were viewed more in the morning (before noon) or in the evening (after 5pm) for eight different universities. The results were as follows:

Morning Evening
Morning Evening
Mean 32 40.625
Variance 89.71428571 504.5536
Observations 8 8
Pearson Correlation 0.343785438
Hypothesized Mean Difference 0
df 7
t Stat -1.152587077
P(T<=t) one-tail 0.143458126
t Critical one-tail 1.894578605
P(T<=t) two-tail 0.286916252
t Critical two-tail 2.364624252
Is there a significant difference between morning and evening access to the university advertisements?
a. Yes, there was a significant difference between Morning (M= 32), and Evening (M=40.625), (t [7] = .28, p < .05).
b. No, there was no difference between Morning (M= 32), and Evening (M=40.625), (t [7] = 1.15, p > .05).
c. Yes, there was a significant difference between Morning (M= 32), and Evening (M=40.625), (t [7] = 1.15 p < .05).
d. No, there was no difference between Morning (M= 32), and Evening (M=40.625), (t [7] = 1.15, p < .05).

Answer 1

b. No, there was no difference between Morning (M= 32), and Evening (M=40.625), (t [7] = 1.15, p > .05).

Explanation:

The critical value for one tailed test is t ∝(7) > 1.895

A one tailed test is performed to test the claim that advertisements were viewed more in the morning (before noon) or in the evening (after 5pm)

The null and alternative hypotheses are

H0: μm = μe vs Ha μm > μe

where μm is the mean of the morning and μe is the mean of evening.

The calculated value of t = -1.152587077 which is less than the critical region hence the null hypothesis cannot be rejected .

P(T<=t) one-tail 0.143458126 > 0.05

If two tailed test is performed the critical region is t Critical two-tail 2.364624252

and the calculated t value is -1.152587077 which again does not lie in the critical region .

Hence μm = μe or μm ≤ μe

P(T<=t) two-tail 0.286916252 > 0.025

Therefore

b. No, there was no difference between Morning (M= 32), and Evening (M=40.625), (t [7] = 1.15, p > .05).

Option b gives the best answer.