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   Volts
1   123.9
2   123.9
3   123.9
4   123.9
5   123.4
6   123.3
7   123.3
8   123.6
9   123.5
10   124.4
11   123.5
12   123.7
13   124.2
14   123.7
15   123.9
16   124.0
17   124.2
18   123.9
19   123.8
20   123.8
21   124.0
22   123.9
23   123.6
24   123.9
25   123.4
26   123.4
27   123.4
28   123.4
29   123.3
30   123.5
31   123.5
32   123.6
33   123.6
34   123.9
35   123.9
36   123.8
37   123.9
38   123.7
39   123.8
40   123.8

1. Calculate the test statistic

2. What is the range of P-value

a. P-value<0.01

b. P-value > 0.20

c. 0.025 < P-value < 0.05

d. 0.05 < P-value < 0.10

e. 0.10 < P-value < 0.20

f. 0.01 < P-value < 0.025

3. Identify the critical value(s)

Answer 1

Using R studio ,we get the following information about given data ( we can do it manually also )

Sample mean, = 123.7275

Sample standard deviation, = 0.2660

Sample size , = 40

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ = 120

Ha: μ ≠ 120

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

Test Statistics

The t-statistic is computed as follows:

The degree of freedom, df = n -1 = 40 - 1 = 39

Corresponding to df =39 and t = 88.627 , the p- value , using t table

p-value

Based on the information provided, the significance level is for α=0.05 and the df = 39 , the critical value for a two-tailed test is

t_c​= 2.023

Answers :

1. The test statistic = 88.627

2. The range of P-value

a. P-value<0.01

3. The critical value = 2.023