Question

A study is conducted to determine if a newly designed text book is more helpful to learning the material than the old edition. The mean score on the final exam for a course using the old edition is 75. Ten randomly selected people who used the new text took the final exam. Their scores are shown in the table below.

Person	A	B	C	D	E	F	G	H	I	J
Test Score	80	85	73	68	92	89	79	70	94	96

Use a 0.05 significance level to test the claim that people do better with the new edition. Assume that the scores are normally distributed and that the population standard deviation is 10.6.

(a) What kind of test should be used?

A. Two-Tailed
B. One-Tailed
C. It does not matter.

(b) The test statistic is (rounded to 2 decimals).

(c) The P-value is

(d) Is there sufficient evidence to support the claim that people do better than 75 on this exam?

A. No
B. Yes

(e) Construct a 9595% confidence interval for the mean score for students using the new text.

Answer 1

(a) We use a one tailed test (since we want to know if the new set of students did better or scored more than 75)

 

(b) From the given data:

= 82.6, s = 10.16

Since n < 30, we use the students t test

The test statistic is given by the equation:

 

(c) The p value, right tailed for degrees of freedom = n - 1 = 9 is 0.0210

 

(d) Since p value is < 0.05, Option A: yes, there is sufficient evidence to support the claim.

 

(e) The 95% CI

the t critical for df = 9 is 2.262

The Lower Limit = - tcritical * s / sqrt(n) = 82.6 - 2.262 * 10.16 / sqrt(10) = 82.6 - 7.27 = 75.33

The Upper Limit = + tcritical * s / sqrt(n) = 82.6 + 2.262 * 10.16 / sqrt(10) = 82.6 + 7.27 = 89.87

The 95% CI is (75.33, 89.87)