Question

Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Refer to the accompanying data set. Use a 0.01 significance level to test the claim that the sample of home voltages and the sample of generator voltages are from populations with the same mean. If there is a statistically significant difference, does that difference have practical significance?

Day    Home (volts)   Generator (volts)
1   123.7   124.2
2   123.9   124.0
3   123.3   125.2
4   123.4   124.3
5   123.3   124.7
6   123.8   124.1
7   123.3   125.4
8   123.8   124.5
9   123.3   124.3
10   123.2   124.7
11   123.4   124.8
12   123.5   124.8
13   123.7   124.7
14   123.9   124.4
15   123.8   124.5
16   123.6   124.6
17   123.5   124.0
18   123.1   124.4
19   123.4   124.7
20   123.8   124.6
21   123.6   124.1
22   123.9   124.2
23   123.6   124.9
24   123.5   124.5
25   123.8   124.6
26   123.4   124.5
27   123.9   124.3
28   123.6   124.5
29   123.7   124.7
30   124.0   124.6
31   123.8   124.6
32   123.2   124.2
33   123.3   124.3
34   123.5   124.3
35   123.6   124.8
36   123.6   124.4
37   123.3   124.4
38   123.3   124.3
39   123.8   125.0
40   123.4   124.2

a.

Let muμ1be the population mean home voltage and letmuμ2 be the population mean generator voltage. What are the null and alternative hypotheses?

b. Calculate the test statistic

c. Find the P Value

d. Make a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

(Reject/no reject) H0. There (is/is not) sufficient evidence to warrant rejection of the claim that the sample of home voltages and the sample of generator voltages are from populations with the same mean. The difference (is/is not) statistically significant.

e. If there is a statistically significant difference, does that difference have practical significance?

A. The sample means suggest that the difference does not have practical significance. The generator could be used as a substitute when needed.

B. The sample means suggest that the difference does have practical significance. The generator could not be used as a substitute when needed.

C. The sample means suggest that the difference does not have practical significance. The generator could not be used as a substitute when needed.

D. The difference is not statistically significant

Answer 1

First we need to find the mean and SD of the data:

Descriptive statistics
	Home	Generator
count	40	40
mean	123.563	124.508
sample standard deviation	0.238	0.308
sample variance	0.057	0.095
minimum	123.1	124
maximum	124	125.4
range	0.9	1.4

(a-c)

(d)

Reject H0. There is sufficient evidence to warrant rejection of the claim that the sample of home voltages and the sample of generator voltages are from populations with the same mean. The difference is statistically significant.

(e)

A. The sample means suggest that the difference does not have practical significance. The generator could be used as a substitute when needed.