AP Statistics T- test

Question

An institute hosted 10 French teachers for 4 weeks.  At the beginning of the period, the teachers were given the Modern Language Association's listening test of understanding of spoken French.  After the 4 weeks of classes, the listening test was given again.  (The actual French spoken in the 2 tests was different, so that simply taking the first test should not improve the score on the second test.) The table below gives the pretest and post test scores.  The maximum possible score on the test is 36.

 

 

Teacher        Pretest         Posttest

1.            32                34
2.            31                31
3.            29                35
4.            10                16
5.            30                33
6.            33                36
7.            22                24 
8.            25                28
9.            32                26
10.            20                26

 

We hope to show that attending the institute improves listening skills.

A)Carry out a 95% confidence Interval for the gain in listening skills.

B)Using your interval, explain if your interval supports the claim that the institute improves listening skills

 

 

Answer 1

before..after...difference

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

 

Mean difference = 2.5

Std Dev of differences SD = 3.5978

Standard Error = SE = SD/sqrt(n) = 1.1377

 

The 95% t for 9 df (df=n-1) is 2.2622 (from Excel function "=TINV(.05,9)")

 

95% CI:

Lower Limit = Mean - t*SE = 2.50 - 2.2622(3.5978) = -0.03737

Upper Limit = Mean + t*SE = 5.0737

 

Since the 95% CI contains a value of zero, we cannot conclude that there is a significant difference between the before and after scores at the alpha=.05 level. In other words, if the true population difference score was zero, we would expect to get this result more than 5 times out of 100.