Question

The accompanying data table lists measured voltage amounts supplied directly to a​ family's home. The power supply company states that it has a target power supply of 120 volts. Using those home voltage​ amounts, test the claim that the mean is 120 volts. Use a 0.01 significance level.

Day 1 Volts 124.2

2 123.9

3 123.9

4 124.3

5 123.4

6 123.3

7 123.3

8 123.6

9 123.5

10 123.7

11 123.5

12 123.7

13 123.8

14 123.7

15 123.9

16 124.0

17 124.2

18 124.3

19 123.8

20 123.8

21 124.0

22 123.9

23 123.6

24 124.4

25 123.4

26 123.4

27 123.4

28 123.4

29 123.3

30 123.8

31 123.5

32 123.6

33 123.7

34 123.9

35 123.9

36 123.8

37 123.9

38 123.7

39 123.8

40 123.8

Answer 1

To test against

Here

sample mean

sample standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 1% significance level if p-value < 0.01

Now,

The value of the test statistic

and p-value

Since p-value < 0.01, so we reject H₀ at 1% significance level and we can conclude that the mean is significantly different from 120 volts