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. Yes
B. No


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 94 102 90 84 115 79 108 105 125 100 Test B 98 102 94 86 115 81 107 105 125 101

Explanation / Answer

The statistical software output for this problem is:

closemaximize

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,

1. a) Matched Pair

b) Test statistic = -2.167 (Rounded off to 3 decimal places)

c) p - value = 0.0292 (Rounded off to 4 decimal places)

d) Yes

2. 95% confidence interval:

(-2.453, 0.053) [Rounded off to 3 decimal places]

Difference Mean Std. Err. DF T-Stat P-value Test A - Test B -1.2 0.55377492 9 -2.1669454 0.0292

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