Question

In an effort to improve the mathematical skills of 12 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 an increase in the scores. at αα =0.05. 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
64	57
99	94
61	62
48	46
99	96
64	69
89	84
69	79
61	66
73	80
90	90
68	75

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 0.05 the critical value is 1.796

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

Answer 1

The statistical software output for this problem is:

From above output:

Hypotheses:

H0:μd≤0H0:μd≤0
HA:μd>0HA:μd>0 (claim)

Option B is correct.

Test statistic = 0.668

P - value = 0.259

Do not reject Ho

There is not enough evidence to support the claim that there was an increase in the scores.