Question

To carry the Energy Star Logo, a 25 cubic-foot French-door refrigerator must use no more than 574 kW-h/year (ignore the weird units). If they use significantly more than that, they are removed from the list (which recently happened). A sample of 23 refrrigerators o fac ertain modle is tested by an independent company. They are found to use an average of 596 kW-h/year, with a sample standard deviation of 18.7 kW-h/year.

a) Write the hypotheses being tested.

b) Give a p-value range for this claim. is it significant at the a=.05 level, using that level what do you conclude?

c) Before the government makes a final decision, they will do their own study of the same model, but we want to get the margin of error down to 10 kW-h/year. How many refrigerators should they test, assuming a=.05 and that the standard deviation will be about the same as the first study (18.7 kW-h/years)?

Answer 1

Solution:-

a)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u < 574
Alternative hypothesis: u > 574

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 3.8992
DF = n - 1

D.F = 22
t = (x - u) / SE

t = 5.64

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of 5.64.

b)

Thus the P-value in this analysis is less than 0.001.

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that French-door refrigerator are not using more than 574 kW-h/year.

c) The number of refrigerators should they test is 14.

n = 13.43

n = 14