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 Television Gross Revenue ($1,000s) 96 91 95 92 95 94 94 94 Newspaper Advertising Advertising ($1,000s) ($1,000s) 5 2 4 2.5 3 3.5 2.5 3 1.5 2 1.5 2.5 3.2 2.3 4.1 2.5 (a) Use a = 0.01 to test the hypotheses Ho: P₁= P₂ = 0 Ha: ₁ and/or ₂ is not equal to zero for the model y =B₁ + B₁X₁ + B₂X₂ + €, 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.)
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 Television Gross Revenue ($1,000s) 96 91 95 92 95 94 94 94 Newspaper Advertising Advertising ($1,000s) ($1,000s) 5 2 4 2.5 3 3.5 2.5 3 1.5 2 1.5 2.5 3.2 2.3 4.1 2.5 (a) Use a = 0.01 to test the hypotheses Ho: P₁= P₂ = 0 Ha: ₁ and/or ₂ is not equal to zero for the model y =B₁ + B₁X₁ + B₂X₂ + €, 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.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Hypothesis Testing for the Significance of β₁**
**(b) Use α = 0.05 to test the significance of β₁.**
**State the null and alternative hypotheses.**
1. \( H_0: \, \hat{\beta}_1 = 0 \)
\( H_a: \, \hat{\beta}_1 < 0 \)
2. \( H_0: \, \hat{\beta}_1 = 0 \)
\( H_a: \, \hat{\beta}_1 \neq 0 \) (Selected option)
3. \( H_0: \, \hat{\beta}_1 = 0 \)
\( H_a: \, \hat{\beta}_1 > 0 \)
4. \( H_0: \, \hat{\beta}_1 \neq 0 \)
\( H_a: \, \hat{\beta}_1 = 0 \)
5. \( H_0: \, \hat{\beta}_1 < 0 \)
\( H_a: \, \hat{\beta}_1 = 0 \)
**Find the value of the test statistic. (Round your answer to two decimal places.)**
[Blank space for answer]
**Find the p-value. (Round your answer to three decimal places.)**
p-value = 0.000
**State your conclusion.**
1. Do not reject \( H_0 \). There is insufficient evidence to conclude that \( \hat{\beta}_1 \) is significant.
2. Reject \( H_0 \). There is insufficient evidence to conclude that \( \hat{\beta}_1 \) is significant.
3. Do not reject \( H_0 \). There is sufficient evidence to conclude that \( \hat{\beta}_1 \) is significant.
4. **Reject \( H_0 \). There is sufficient evidence to conclude that \( \hat{\beta}_1 \) is significant.** (Selected option)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2fdea76-24b5-4e92-ab93-0d275ab88ec3%2Fdc0b114d-3332-4cd2-a501-59508d3b717a%2F38xji96_processed.png&w=3840&q=75)
Transcribed Image Text:**Hypothesis Testing for the Significance of β₁**
**(b) Use α = 0.05 to test the significance of β₁.**
**State the null and alternative hypotheses.**
1. \( H_0: \, \hat{\beta}_1 = 0 \)
\( H_a: \, \hat{\beta}_1 < 0 \)
2. \( H_0: \, \hat{\beta}_1 = 0 \)
\( H_a: \, \hat{\beta}_1 \neq 0 \) (Selected option)
3. \( H_0: \, \hat{\beta}_1 = 0 \)
\( H_a: \, \hat{\beta}_1 > 0 \)
4. \( H_0: \, \hat{\beta}_1 \neq 0 \)
\( H_a: \, \hat{\beta}_1 = 0 \)
5. \( H_0: \, \hat{\beta}_1 < 0 \)
\( H_a: \, \hat{\beta}_1 = 0 \)
**Find the value of the test statistic. (Round your answer to two decimal places.)**
[Blank space for answer]
**Find the p-value. (Round your answer to three decimal places.)**
p-value = 0.000
**State your conclusion.**
1. Do not reject \( H_0 \). There is insufficient evidence to conclude that \( \hat{\beta}_1 \) is significant.
2. Reject \( H_0 \). There is insufficient evidence to conclude that \( \hat{\beta}_1 \) is significant.
3. Do not reject \( H_0 \). There is sufficient evidence to conclude that \( \hat{\beta}_1 \) is significant.
4. **Reject \( H_0 \). There is sufficient evidence to conclude that \( \hat{\beta}_1 \) is significant.** (Selected option)
![## Understanding the Relationship Between Advertising and Weekly Gross Revenue
A statistical program is recommended.
The owner of a movie theater company is interested in predicting weekly gross revenue as a function of advertising expenditures. Below is historical data for a sample of eight weeks:
| 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 | 2.3 |
| 94 | 2.5 | 4.1 |
| 94 | 3 | 2.5 |
### Statistical Hypothesis Testing
(a) **Use \(\alpha = 0.01\) to test the hypotheses:**
- \( H_0: \beta_1 = \beta_2 = 0 \)
- \( H_a: \beta_1 \) and/or \( \beta_2 \) is not equal to zero
For the model:
\[ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \varepsilon \]
where:
- \( x_1 = \) television advertising ($1,000s),
- \( x_2 = \) newspaper advertising ($1,000s).
Find the value of the test statistic. (Round your answer to two decimal places.)
---
In the table, each row represents one week of data, capturing the weekly gross revenue in relation to the expenditures on television and newspaper advertising. The objective is to understand how these advertising expenditures impact the revenue. Statistical tests will help determine if there is a significant relationship.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2fdea76-24b5-4e92-ab93-0d275ab88ec3%2Fdc0b114d-3332-4cd2-a501-59508d3b717a%2F2o7xgic_processed.png&w=3840&q=75)
Transcribed Image Text:## Understanding the Relationship Between Advertising and Weekly Gross Revenue
A statistical program is recommended.
The owner of a movie theater company is interested in predicting weekly gross revenue as a function of advertising expenditures. Below is historical data for a sample of eight weeks:
| 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 | 2.3 |
| 94 | 2.5 | 4.1 |
| 94 | 3 | 2.5 |
### Statistical Hypothesis Testing
(a) **Use \(\alpha = 0.01\) to test the hypotheses:**
- \( H_0: \beta_1 = \beta_2 = 0 \)
- \( H_a: \beta_1 \) and/or \( \beta_2 \) is not equal to zero
For the model:
\[ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \varepsilon \]
where:
- \( x_1 = \) television advertising ($1,000s),
- \( x_2 = \) newspaper advertising ($1,000s).
Find the value of the test statistic. (Round your answer to two decimal places.)
---
In the table, each row represents one week of data, capturing the weekly gross revenue in relation to the expenditures on television and newspaper advertising. The objective is to understand how these advertising expenditures impact the revenue. Statistical tests will help determine if there is a significant relationship.
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