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

(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. No
B. Yes


2. Construct a 95% 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 89 83 119 127 75 112 97 101 106 94 Test B 88 83 120 130 75 115 101 106 110 94

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:

95% confidence interval results:

Hence,

The answers will be:

a) Test method: Option A; Matched pairs

b) Test statistic = -2.82

Critical value = -1.833

d) Yes

2. 95% confidence interval:

(-3.425, -0.375)

Difference Mean Std. Err. DF T-Stat P-value Test A - Test B -1.9 0.67412495 9 -2.8184686 0.01

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