Question

In: Statistics and Probability

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

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

Solutions

Expert Solution

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


Related Solutions

Ten randomly selected people took an IQ test A, and next day they took a very...
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 81 105 91 116 102 74 95 122 99 112 Test B 84 105 89 122 103 77 98 122 102 116 1. Consider (Test A - Test B). Use a 0.050.05 significance level to test the claim that...
Ten randomly selected people took an IQ test A, and next day they took a very...
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 123 97 112 89 103 94 74 119 85 105 Test B 122 100 110 89 102 92 73 121 87 104 The test statistic is _ The critical value is_ Construct a 99% confidence interval for the mean...
Ten randomly selected people took an IQ test A, and next day they took a very...
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 71 119 104 100 108 127 83 97 94 92 Test B 72 119 110 105 106 130 85 100 92 91 1. Consider (Test A - Test B). Use a 0.05 0.05 significance level to test the claim...
Ten randomly selected people took an IQ test A. The next day they took a very...
Ten randomly selected people took an IQ test A. The next day they took a very similar IQ test B. Their scores are shown in the table below. Person 1 2 3 4 5 6 7 8 9 10 Test A 106 99 95 92 87 127 115 100 77 108 Test B 112 101 99 96 90 130 112 99 80 112 1. Use a 0.05 significance level to test the claim that, on average, people do better on...
Ten randomly selected people took an IQ test A, and next day they took a very...
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 98 107 110 118 125 79 95 101 84 91 Test B 100 106 114 118 124 77 98 99 83 89 1. Consider (Test A - Test B). Use a 0.050.05 significance level to test the claim that...
Ten randomly selected people took an IQ test A, and next day they took a very...
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 106 120 113 75 83 103 111 93 89 99 Test B 104 119 116 78 82 108 108 92 91 98 1. Consider (Test A - Test B). Use a 0.01 significance level to test the claim that...
Ten randomly selected people took an IQ test A, and next day they took a very...
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 100 120 117 107 102 81 90 94 74 112 Test B 102 119 122 105 102 83 95 92 72 109 1. Consider (Test A - Test B). Use a 0.01 significance level to test the claim that...
Ten randomly selected people took an IQ test A, and next day they took a very...
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 98 108 76 82 94 89 127 119 101 108 Test B 97 114 77 82 98 94 129 121 103 106 1. Consider (Test A - Test B). Use a 0.01 0.01 (a) What test method should be...
Ten randomly selected people took an IQ test A, and next day they took a very...
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 95 89 124 105 99 114 108 73 103 84 Test B 99 91 123 110 99 119 105 72 106 86 1. Consider (Test A - Test B). Use a 0.01 significance level to test the claim that...
Ten randomly selected people took an IQ test A, and next day they took a very...
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 119 81 75 125 95 90 106 97 102 109 Test B 116 84 78 125 99 90 106 96 104 113 1. Consider (Test A - Test B). Use a 0.050.05 significance level to test the claim that...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT