Problem 1

The manufacturer of a refrigerator system produces refrigerators that are supposed to maintain an average temperature of 48 F, ideal for certain beverages. The owner of a beverage company is concerned that one of his refrigerators is not maintaining the advertised temperature. He takes 30 temperature readings from his refrigerator at random times over the course of a week and finds a sample mean of 49.2 F, with a standard deviation of 2.1 F.

a.State hypotheses to test whether the owner is correct.

b.Use StatCrunch to find the test statistic and p-value:

Stat T Stats One Sample With Summary

Enter , s, and n from the problem setup.

Under Perform, select Hypothesis test for .

Enter the hypothesized value from your null hypothesis.

Select the correct sign for the alternative hypothesis.

Click Compute!

Report the test statistic and the p-value. (Round to three decimal places.)

c.Using a significance level of 0.01, do you reject H₀?

d.Use StatCrunch to compute a 99% confidence interval for the average temperature of the owner's refrigerator:

Stat T Stats One Sample With Summary

Enter , s, and n from the problem setup.

Under Perform, select Confidence interval for .

Enter the confidence level.

Click Compute!

Report the confidence interval. (Round to two decimal places.)

e.State what the interval means in the context of the problem.

f.If you were the owner of this beverage company, would you be concerned about the temperature difference? Explain. (Consider statistical vs. practical significance.)