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	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 people do better on the second test than they do on the first. Round calculated answers to three decimal places.

(a) What test method should be used?

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

(b) The null hypothesis is μdiff=0μdiff=0. What is the alternate hypothesis?

A. μdiff>0μdiff>0
B. μdiff≠0μdiff≠0
C. μdiff<0μdiff<0

(c) The test statistic is

(d) The p-value is

(e) 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).
<μ<<μ<

Answer 1

The following table is obtained:

	Sample 1	Sample 2	Difference = Sample 1 - Sample 2
	98	100	-2
	107	106	1
	110	114	-4
	118	118	0
	125	124	1
	79	77	2
	95	98	-3
	101	99	2
	84	83	1
	91	89	2
Average	100.8	100.8	0
St. Dev.	14.528	15.164	2.211
n	10	10	10

For the score differences we have

(a) What test method should be used?
C. Matched Pairs

(b) The null hypothesis is μdiff=0. What is the alternate hypothesis?
C. μdiff<0

(c)

The t-statistic is computed as shown in the following formula:

(d) The p-value is 0.5

(e) Is there sufficient evidence to support the claim that people do better on the second test?
B. No

Since it is observed that t=0≥tc​=−1.833, it is then concluded that the null hypothesis is not rejected.It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1​ is less than μ2​, at the 0.05 significance level.

2. Construct a 95% confidence interval for the mean of the differences. Again, use (Test A - Test B).
−1.582<μD​<1.582

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