Question

In an effort to improve the mathematical skills of 18 students, a teacher provides a weekly 1-hour tutoring session. A pre-test is given before the sessions and a post-test is given after. The results are shown here. Test the claim that there was a decrease in the scores. at αα=0.01. You believe that the population is normally distributed, but you do not know the standard deviation. When calculating difference use Post-test minus Pre-test.

pre-test	post-test
43	50
58	65
45	37
50	55
83	90
92	82
55	51
71	66
63	69
88	95
41	41
96	105
74	84
100	106
76	80
99	91
61	52
60	62

Which of the following are the correct hypotheses?

• H0:μd≥0H0:μd≥0
  HA:μd<0HA:μd<0(claim)
• H0:μd≤0H0:μd≤0
  HA:μd>0HA:μd>0(claim)
• H0:μd=0H0:μd=0
  HA:μd≠0HA:μd≠0(claim)

Given that αα is 0.01 the critical value is -2.567

The test statistic is: (round to 3 places)

The p-value is: (round to 3 places)

The decision can be made to:

• reject H0H0
• do not reject H0H0

The final conclusion is that:

• There is enough evidence to reject the claim that there was a decrease in the scores.
• There is not enough evidence to reject the claim that there was a decrease in the scores.
• There is enough evidence to support the claim that there was a decrease in the scores.
• There is not enough evidence to support the claim that there was a decrease in the scores.

Answer 1

Solution:

Install analysis toolpak and then go to

Data >Data analysis>Paired two sample for means

we get

H0:μd≥0

HA:μd<0(claim)

t=0.90

The p-value is: P=0.193

P>0.01

Fail to reject Ho

• There is not enough evidence to support the claim that there was a decrease in the scores.