Question
A statistical program is recommended. The owner of a movie theater company would like to predict weekly gross revenue as a function of advertising expenditures.
A statistical program is recommended.
The owner of a movie theater company would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.
| Weekly Gross Revenue ($1,000s) | Television Advertising ($1,000s) | Newspaper Advertising ($1,000s) |
|---|---|---|
| 96 | 5 | 1.5 |
| 90 | 2 | 2 |
| 95 | 4 | 1.5 |
| 93 | 2.5 | 2.5 |
| 95 | 3 | 3.3 |
| 94 | 3.5 | 2.3 |
| 94 | 2.5 | 4.2 |
| 94 | 3 | 2.5 |
(a)Use = 0.01 to test the hypotheses
| H0: | 1 = 2 = 0 |
| Ha: | 1 and/or 2 is not equal to zero |
for the model
y = 0 + 1x1 + 2x2 + ,
where
| x1 | = | television advertising ($1,000s) |
| x2 | = | newspaper advertising ($1,000s). |
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to three decimal places.)p-value =
State your conclusion.
Do not reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables.
Reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables.
Reject H0. There is insufficient evidence to conclude that there is a significant relationship among the variables.
Do not reject H0. There is insufficient evidence to conclude that there is a significant relationship among the variables.
(b)Use = 0.05 to test the significance of 1.
State the null and alternative hypotheses.
| H0: 1 = 0 |
| Ha: 1 < 0 |
| H0: 1 0 |
| Ha: 1 = 0 |
| H0: 1 < 0 |
| Ha: 1 = 0 |
| H0: 1 = 0 |
| Ha: 1 > 0 |
| H0: 1 = 0 |
| Ha: 1 0 |
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to three decimal places.)p-value =
State your conclusion.
Do not reject H0. There is insufficient evidence to conclude that 1 is significant.
Reject H0. There is sufficient evidence to conclude that 1 is significant.
Reject H0. There is insufficient evidence to conclude that 1 is significant.
Do not reject H0. There is sufficient evidence to conclude that 1 is significant.
Should x1 be dropped from the model?
Yes/No
(c)Use = 0.05 to test the significance of 2.
State the null and alternative hypotheses.
| H0: 2 = 0 |
| Ha: 2 0 |
| H0: 2 = 0 |
| Ha: 2 < 0 |
| H0: 2 0 |
| Ha: 2 = 0 |
| H0: 2 = 0 |
| Ha: 2 > 0 |
| H0: 2 < 0 |
| Ha: 2 = 0 |
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to three decimal places.)p-value =
State your conclusion.
Reject H0. There is sufficient evidence to conclude that 2 is significant.
Do not reject H0. There is insufficient evidence to conclude that 2 is significant.
Do not reject H0. There is sufficient evidence to conclude that 2 is significant.
Reject H0. There is insufficient evidence to conclude that 2 is significant.
Should x2 be dropped from the model?
Yes/No
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Statistics Informed Decisions Using Data
Authors: Michael Sullivan
5th Global Edition
9781292157115
