Ten randomly selected people took an IQ test A, and next day they took a very si

Question

Ten randomly selected people took an IQ test A, and next day they took a very similar IQ test B. Their scores are shown in the table below.

1. Consider (Test A - Test B). Use a 0.01 significance level to test the claim that people do better on the second test than they do on the first. (Note: You may wish to use software.)

(a) What test method should be used?

A. Two Sample z
B. Two Sample t
C. Matched Pairs

(b) The test statistic is

(c) The critical value is

(d) Is there sufficient evidence to support the claim that people do better on the second test?

A. Yes
B. No


2. Construct a 99% confidence interval for the mean of the differences. Again, use (Test A - Test B).
<<

Person A B C D E F G H I J Test A 81 116 72 100 110 106 100 129 96 90 Test B 80 113 71 105 112 104 104 130 94 93

Explanation / Answer

The statistical software output for this problem is:

Paired T hypothesis test:
D = 1 - 2 : Mean of the difference between Test A and Test B
H0 : D = 0
HA : D 0
Hypothesis test results:

99% confidence interval results:

Hence,

1. a) Matched Pairs

b) Test statistic = -0.678

c) Critical value = -2.821

d) No

2. 99% confidence interval will be:

-3.474 < < 2.274

Difference Mean Std. Err. DF T-Stat P-value Test A - Test B -0.6 0.88443328 9 -0.67840053 0.5146

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