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 91 2 2 95 4 1.5 92 2.5 2.5 95 3 3.2 94 3.5 2.2 94 2.5 4.2 94 3 2.5 (a) Use ? = 0.01 to test the hypotheses H0: B1 = B2 = 0 Ha: B1 and/or B2 is not equal to zero for the model y = B0 + B1x1 + B2x2 + E, 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.) Statistic=?? 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 a = 0.05 to test the significance of B1. State the null and alternative hypotheses. H0: B1 ≠ 0 Ha: B1 = 0 H0: B1 = 0 Ha: B1 ≠ 0 H0: B1 < 0 Ha: B1 = 0 H0: B1 = 0 Ha: B1 < 0 H0: B1 = 0 Ha: B1 > 0 Find the value of the test statistic. (Round your answer to two decimal places.) Statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Reject H0. There is insufficient evidence to conclude that B1 is significant. -Do not reject H0. There is sufficient evidence to conclude that B1 is significant. - Do not reject H0. There is insufficient evidence to conclude that B1 is significant. -Reject H0. There is sufficient evidence to conclude that B1 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: B2 = 0 Ha: B2 < 0 H0: B2 ≠ 0 Ha: B2 = 0 H0: B2 = 0 Ha: B2 ≠ 0 H0: B2 < 0 Ha: B2 = 0 H0: B2 = 0 Ha: B2 > 0 Find the value of the test statistic. (Round your answer to two decimal places.) Statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ??
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 91 2 2 95 4 1.5 92 2.5 2.5 95 3 3.2 94 3.5 2.2 94 2.5 4.2 94 3 2.5 (a) Use ? = 0.01 to test the hypotheses H0: B1 = B2 = 0 Ha: B1 and/or B2 is not equal to zero for the model y = B0 + B1x1 + B2x2 + E, 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.) Statistic=?? 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 a = 0.05 to test the significance of B1. State the null and alternative hypotheses. H0: B1 ≠ 0 Ha: B1 = 0 H0: B1 = 0 Ha: B1 ≠ 0 H0: B1 < 0 Ha: B1 = 0 H0: B1 = 0 Ha: B1 < 0 H0: B1 = 0 Ha: B1 > 0 Find the value of the test statistic. (Round your answer to two decimal places.) Statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Reject H0. There is insufficient evidence to conclude that B1 is significant. -Do not reject H0. There is sufficient evidence to conclude that B1 is significant. - Do not reject H0. There is insufficient evidence to conclude that B1 is significant. -Reject H0. There is sufficient evidence to conclude that B1 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: B2 = 0 Ha: B2 < 0 H0: B2 ≠ 0 Ha: B2 = 0 H0: B2 = 0 Ha: B2 ≠ 0 H0: B2 < 0 Ha: B2 = 0 H0: B2 = 0 Ha: B2 > 0 Find the value of the test statistic. (Round your answer to two decimal places.) Statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ??
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter7: Integration
Section7.CR: Chapter 7 Review
Problem 88CR
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Question
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 |
| 91 | 2 | 2 |
| 95 | 4 | 1.5 |
| 92 | 2.5 | 2.5 |
| 95 | 3 | 3.2 |
| 94 | 3.5 | 2.2 |
| 94 | 2.5 | 4.2 |
| 94 | 3 | 2.5 |
(a)
Use ? = 0.01 to test the hypotheses
| H0: | B1 = B2 = 0 |
| Ha: | B1 and/or B2 is not equal to zero |
for the model
y = B0 + B1x1 + B2x2 + E,
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.)
Statistic=??
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 a = 0.05 to test the significance of B1.
State the null and alternative hypotheses.
| H0: B1 ≠ 0 |
| Ha: B1 = 0 |
| H0: B1 = 0 |
| Ha: B1 ≠ 0 |
| H0: B1 < 0 |
| Ha: B1 = 0 |
| H0: B1 = 0 |
| Ha: B1 < 0 |
| H0: B1 = 0 |
| Ha: B1 > 0 |
Find the value of the test statistic. (Round your answer to two decimal places.)
Statistic=??
Find the p-value. (Round your answer to three decimal places.)
p-value = ??
State your conclusion.
-Reject H0. There is insufficient evidence to conclude that B1 is significant.
-Do not reject H0. There is sufficient evidence to conclude that B1 is significant.
- Do not reject H0. There is insufficient evidence to conclude that B1 is significant.
-Reject H0. There is sufficient evidence to conclude that B1 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: B2 = 0 |
| Ha: B2 < 0 |
| H0: B2 ≠ 0 |
| Ha: B2 = 0 |
| H0: B2 = 0 |
| Ha: B2 ≠ 0 |
| H0: B2 < 0 |
| Ha: B2 = 0 |
| H0: B2 = 0 |
| Ha: B2 > 0 |
Find the value of the test statistic. (Round your answer to two decimal places.)
Statistic=??
Find the p-value. (Round your answer to three decimal places.)
p-value = ??
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