Question

20. Run the same data from question 19 (and the same criteria) using a repeated measures t test.
a. Perform the test and report results (show ALL work)
b. Explain what the difference in results is due to.

19. A teacher wanted to test that if telling students that a test would be curved to the highest grade would help them perform better on quizzes. She gave quizzes to two groups of 5 students each and told one that there would be a curve and the other group was told there would be no curve given. Following are the scores on the quizzes for the two groups:

Yes curve: 75, 80, 78, 87, 90
No curve: 76, 83, 72, 80, 70
Run an independent t test on the data and report the test results using an alpha level of .05. Show ALL work.

Answer 1

19)

Hypothesis:

where is the mean score by yes curve group and   is the mean score obtained by no curve group

This is a right-tailed test.

The significance level = 0.05

Test statistic

The t statistic is obtained using the formula,

From data values,

	Yes curve	No curve
mean	82	76.2
stddev	6.2849	5.4037
n	5	5

P-value

The P-value for the t statistic is obtained from the t distribution table for the degree of freedom = n1+n2-2=8

Conclusion

Since the P-value is greater than 0.05 at the 5% significance level for the one-sided alternative hypothesis, the null hypothesis is not rejected. Hence, it can be concluded that the curved to the highest grade would help students perform better on quizzes

20)

a)

Hypothesis:

where is the mean difference in the quiz scores

This is a right-tailed test.

The significance level = 0.05

Test statistic

The t-statistic is obtained using the formula,

From the data values,

Yes curve	No curve	Difference
75	76	-1
80	83	-3
78	72	6
87	80	7
90	70	20
	Average	5.8
	StdDev	9.0388

P-value

The P-value for t = 1.4348 is obtained from the t-distribution table for the degree of freedom = n - 1 = 4 for one-tailed hypothesis,

Conclusion

Since the P-value is greater than 0.05 at the 5% significance level for the one-sided alternative hypothesis, the null hypothesis is not rejected. Hence, it can be concluded that the curved to the highest grade would help students perform better on quizzes

b)

From the above two tests,

	t Stat	P-value		sign. level
Independent sample t-test	1.5647	0.0781	>	0.05	not significant
Paired sample t-test	1.4348	0.1123	>	0.05	not significant

The independent-sample t-test compares the two independent groups mean and the paired sample t-test test whether the paired wise mean difference is zero or not. Since the paired sample test takes the pair-wise, it eliminates the errors caused by individuals hence the improves the test result.

The t statistic is decreased in the paired t-test and thus the p-value increased.