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 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 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. No

B. Yes

2. Construct a 99

99

<μ<

<

μ

<

Answer 1

We are given the two tests were similar. So, it means we have to use a matched pair test.

1. Consider (Test A - Test B). Use a 0.01

(a) What test method should be used?

Matched Pairs is the correct test method because the data is similar in nature.

Load the data into Excel.

Go to Data>Megastat.

Select the option Hypothesis tests and go to Paired Observations.

Select the Group 1 and Group 2 as Test A and Test B data set respectively.

Click OK.

The output obtained will be as follows:

0.000	hypothesized value
100.200	mean Test A
102.100	mean Test B
-1.900	mean difference (Test A - Test B)
2.558	std. dev.
0.809	std. error
10	n
9	df
-2.349	t
.0217	p-value (one-tailed, lower)
-2.8214	t Critical one-tail
-4.529	confidence interval 99.% lower
0.729	confidence interval 99.% upper
2.629	margin of error

The hypothesis for testing is:

Paired T hypothesis test:
μ_D = μ₁ - μ₂: Mean of the difference between Test A and Test B
H₀ : μ_D = 0

People do good on both tests.
H_A : μ_D < 0

People do better on the second test.

(b) The test statistic from the output is -2.349.

(c) The critical value from the output is -2.8214.

(d) Since |t_statistic| < t_critical, we fail to reject the null hypothesis.

So, there is not sufficient evidence to support the claim that people do better on the second test.

Therefore, the correct answer is No.

2. Construct a 99% confidence interval.

The 99% confidence interval from the output is between -4.529 and 0.729.