Question

The National Endowment for the Humanities sponsors summer institutes to improve the skills of high school teachers of foreign languages. At the beginning of the period, the teachers were given the Modern Language Association’s listening test of understanding of spoken French. A random sample of 15 teachers’ test score was collected. After 4 weeks of immersion in French in and out of class, the listening test was given again. From the second test results, another 15 3 teachers’ test scores were randomly and independently collected. The maximum possible score of the test is 36. The data follow.

Use the summary statistics to conduct the most appropriate test to determine whether the course improves French spoken-language skills. Use α = 0.01.

First test	second test
32	34
31	31
29	35
10	16
30	33
33	36
22	24
25	28
32	26
20	26
20	18
27	24
31	32
26	23
15	19

Answer 1

First test	Second test	Difference(d)
32	34	-2
31	31	0
29	35	-6
10	16	-6
30	33	-3
33	36	-3
22	24	-2
25	28	-3
32	26	6
20	26	-6
20	18	2
27	24	3
31	32	-1
26	23	3
15	19	-4
	Total	-22

Claim: The course improves French spoken-language skills.

The null and alternative hypothesis is

Level of significance = 0.01

Sample size = n = 15

Sample mean of difference = = - 1.4667

Sample standard deviation of difference = = 3.6423

Test statistic is

Degrees of freedom = n - 1 = 15 - 1 = 14

Level of significance = 0.01

Critical value = 2.977 ( Using t table)

Test statistic | t | < critical value we fail to reject null hypothesis.

Conclusion: The course NOT improves French spoken-language skills.