Question

Preliminary data analyses indicates that use of a paired t-test is reasonable. Perform the hypothesis test by using either the critical-value approach or the P-value approach as indicated. Assume that the null hypothesis is Ho:u1=u2

Five students took a math test before and after tutoring. Their scores were as follows.

  

subject	A	B	C	D	E
Before	73	66	76	69	72
After	77	75	74	72	84

At the 1% significance level, do the data provide sufficient evidence to conclude that the mean score before tutoring differs from the mean score after tutoring? Use the P-value approach.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ(d) = 0
Alternative Hypothesis: μ(d) ≠ 0

Test statistic,
t = (dbar - 0)/(s(d)/sqrt(n))
t = (-5.2 - 0)/(5.4498/sqrt(5))
t = -2.134

P-value Approach
P-value = 0.0998
As P-value >= 0.01, fail to reject null hypothesis.