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. Person A B C D E F G H I J Test A 71 84 105 99 93 119 101 126 108 90 Test B 72 86 107 102 92 120 106 128 107 95 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 t B. Two Sample z 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). <μ

Answer 1

Solution:

here sample sizes are small.n1,n2<30

use t test for independent samples as Test A,Test B are independent samples

Two Sample t

use Excel

t-Test: Two-Sample Assuming Equal Variances
	Test_A	Test_B
Mean	99.6	101.5
Variance	263.6	263.1667
Observations	10	10
Pooled Variance	263.3833
Hypothesized Mean Difference	0
df	18
t Stat	-0.26178
P(T<=t) one-tail	0.39823
t Critical one-tail	2.55238
P(T<=t) two-tail	0.79646
t Critical two-tail	2.87844

b) The test statistic is

test statistc: t = -0.26178

) The critical value is

t Critical one-tail   2.55237963

t stat< t crit

Fail to reject null hypothesis

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

NO

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

Using R studio:

Test_A <- c(71, 84, 105, 99 ,93, 119, 101 ,126 ,108, 90)
Test_B <- c(72,86, 107, 102, 92, 120, 106 ,128, 107, 95)
t.test(Test_A,Test_B,conf.level=0.99)

Ouptut:

Welch Two Sample t-test

data: Test_A and Test_B
t = -0.26178, df = 18, p-value = 0.7965
alternative hypothesis: true difference in means is not equal to 0
99 percent confidence interval:
-22.79135 18.99135
sample estimates:
mean of x mean of y
99.6 101.5

99 percent confidence interval lie sin between
-22.79135 and 18.99135