Question

Refer to the accompanying data set. Use a 0.05 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?

Let μ₁ be the population mean home voltage and let μ₂ be the population mean generator voltage. What are the null and alternative​ hypotheses?

Calculate the test statistic.

t = ____ ​(Round to three decimal places as​ needed.)

Find the​ P-value.

​P-value = ____ ​(Round to four decimal places as​ needed.)

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

(Fail to reject or Reject) H₀. There (is not or 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 or is not) statistically significant.

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 have practical significance. The generator could be used as a substitute when needed.

D. The difference is not statistically significant.

Day    Home (volts)     Generator (volts)

1            123.4 124.8

2            123.6 124.5

3            123.6 125.3

4            124.0   124.7

5            123.3   125.2

6            123.5 124.3

7            123.1 125.0

8            123.6 124.3

9            123.8 124.0

10          123.1 124.2

11          123.7 124.4

12          123.3 124.8

13          123.2    124.1

14          123.9 124.2

15          123.8 124.6

16          123.7 124.7

17          124.1 124.3

18          123.9 124.4

19          123.9 124.7

20          123.2 124.4

21          123.7 124.8

22          123.0 124.8

23          123.3 124.4

24          123.5 124.9

25          123.8 124.8

26          123.7 124.7

27          123.8 124.8

28          123.7 124.8

29          123.2 124.4

30          123.2 124.1

31          123.7 124.9

32          123.9   125.0

33          123.4 124.1

34          123.8 124.7

35          123.1 124.0

36          123.0 124.2

37          123.9 124.1

38          123.8 125.0

39          123.1 124.6

40          123.4 124.9

Answer 1

from above:

t=0.589

​P-value =0.5596

Fail to reject , there 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 not statistically significant

D. The difference is not statistically significant.