Question

It is claimed that an energy star refrigerator uses 46 kWh per month. A random sample of 12 homes indicates that energy star refrigerators in those homes expend an average of 42 kWh per month with a standard deviation 11.9 kWh. Does this suggest that, on average, energy star refrigerators expend 46 kWh per year at the .01 significance level?

Answer 1

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

H0: µ = 46 versus Ha: µ ≠ 46

This is a two tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 46

Xbar = 42

S = 11.9

n = 12

df = n – 1 = 11

α = 0.01

Critical value = - 3.1058 and 3.1058

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (42 - 46)/[11.9/sqrt(12)]

t = -1.1644

P-value = 0.2689

(by using t-table)

P-value > α = 0.01

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that on average, energy star refrigerators expend 46 kWh per year at the .01 significance level.