Discussion:
"The Florida Home Energy Commission lists the mean annual air-conditioning (A/C) expenditure for a well-insulated Central Florida home as $1.20 per square foot. Cool Crib Insulation (a home insulation company) is working hard to attract new customers. In the company's advertising, they claim that homes with their exclusive, patented insulation material have A/C costs that are below average for the region. A consumer-affairs investigator has surveyed a sample of 80 recent Cool Crib customers and listed their A/C expenditures (per square foot) in the following tab. The investigator is interested in examining whether the mean A/C expenditures for Cool Crib's clients really is less than the $1.20 per square foot average for the entire region. Based on these data, and using a significance level of 5% provide the answers to the following questions in the spaces provided:
Report all answers to this problem to a minimum of 4 decimal places.
Using the provided sample data,(in the attached excel spreadsheet), to response the following questions:
a. Write the expression for the correct alternative hypothesis statement for the test that must be carried out.
b. Perform the hypothesis test and record the "p-value" for this test.
c. Which of the following statements is correct?
i) The mean annual A/C expenditure for Cool Crib clients appears to be significantly less than the regional average of $1.20 per square foot.
ii) The mean annual A/C expenditure for Cool Crib clients appears NOT to be significantly less than the regional average of $1.20 per square foot.
d. The investigator would next (separately) like to estimate, with 99% confidence, the mean annual A/C expenditures for all Cool Crib clients. Based on the same sample data (used in parts a. thru c. above), find the range in which he can be 99% confident that the actual mean annual A/C expenditures (for all Cool Crib clients) will fall?
Annual A/C Expense (per square foot) from sample of Cool Crib customers
| 1.14 |
| 1.47 |
| 1.49 |
| 1.06 |
| 0.83 |
| 1.30 |
| 0.98 |
| 1.27 |
| 1.25 |
| 0.97 |
| 0.94 |
| 1.44 |
| 0.87 |
| 1.34 |
| 0.99 |
| 1.02 |
| 1.04 |
| 0.86 |
| 1.23 |
| 0.71 |
| 1.51 |
| 1.23 |
| 1.38 |
| 1.16 |
| 1.23 |
| 1.38 |
| 1.00 |
| 1.20 |
| 1.52 |
| 1.20 |
| 1.07 |
| 1.45 |
| 1.00 |
| 0.94 |
| 0.89 |
| 1.46 |
| 1.32 |
| 0.97 |
| 0.94 |
| 1.40 |
| 1.13 |
| 1.30 |
| 1.11 |
| 1.34 |
| 0.75 |
| 1.37 |
| 1.01 |
| 1.50 |
| 1.18 |
| 1.06 |
| 0.96 |
| 1.13 |
| 1.21 |
| 1.29 |
| 1.43 |
| 1.38 |
| 1.02 |
| 1.27 |
| 1.09 |
| 1.56 |
| 1.35 |
| 1.26 |
| 1.38 |
| 0.98 |
| 1.16 |
| 1.19 |
| 0.93 |
| 1.56 |
| 0.84 |
| 0.80 |
| 1.17 |
| 1.33 |
| 0.79 |
| 1.10 |
| 1.04 |
| 1.05 |
| 1.01 |
| 1.05 |
| 1.20 |
| 0.91 |