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.


Volts

 123.6 123.9 123.9 123.7 123.4 123.3 123.3 123.6 123.5 123.9 123.5 123.7 124.4 123.7 123.9 124.0 124.2 123.7 123.8
 123.8 124.0 123.9 123.6 124.2 123.4 123.4 123.4 123.4 123.3 123.7 123.5 123.6 124.2 123.9 123.9 123.8 123.9 123.7 123.8 123.8

Answer 1

Given:
The sample array is
x = [123.6 123.9 123.9 123.7 123.4 123.3 123.3 123.6 123.5 123.9      123.5 123.7 124.4 123.7 123.9 124.0 124.2 123.7 123.8 123.8      124.0 123.9 123.6 124.2 123.4 123.4 123.4 123.4 123.3 123.7 
     123.5 123.6 124.2 123.9 123.9 123.8 123.9 123.7 123.8 123.8]

From the calculator,
The sample size is
n = 40
The sample mean is
xavg = 123.73
The sample std. deviation is
s = 0.27

The expected population average is
μ = 120

Calculate the test statistic.
z = (xavg - μ)/(s/√n) .
   = (123.73 - 120)/(0.27/√40)
   =   87.36

The null hypothesis is
H₀: xavg = μ
and the alternate hypothesis is
xavg > μ

At α=0.01 level of significance, the one-tailed test has a rejection region of 
α/2 = 0.005.
From standard tables, the test statistic clearly falls in the rejection region.
We should reject the null hypothesis and conclude that xavg > μ.

Answer:
The claim that the mean voltage is 120 V is false at the 0.01 significance level.