A colleague claims that he is 90% sure that advertising does not improve sales and in fact, it might even diminish your revenues. Can you reject his null hypothesis? Explain calculating the test statistic and setting up the hypothesis test correctly (H0: β1 ≤ 0) **Table Title:** Sample Data for Sales (y) and Number of Ads (x)This table provides data from six advertising campaigns, showing the number of ads (x) and the resulting sales revenues (y). Variables are defined as follows:- **Obs.:** Observation number- **x:** Number of ads- **y:** Sales revenue- \(x_i - \bar{x}\): Difference between individual x values and the mean of x- \((x_i - \bar{x})^2\): Square of the deviation of x- \(y_i - \bar{y}\): Difference between individual y values and the mean of y- \((x_i - \bar{x})(y_i - \bar{y})\): Product of deviations from the mean for x and y- \(\hat{y}_i\): Predicted y value- \(e_i\): Error term (difference between actual and predicted y values)- \((y_i - \bar{y})^2\): Square of the deviation of y- \((\hat{y}_i - \bar{y})^2\): Square of the deviation of predicted y**Observations:**1. **Observation 1:** - x = 10, y = 492. **Observation 2:** - x = 6, y = 413. **Observation 3:** - x = 16, y = 494. **Observation 4:** - x = 8, y = 365. **Observation 5:** - x = 12, y = 466. **Observation 6:** - x = 8, y = 43This table allows analysis of the relationship between the number of ads and sales revenue, incorporating statistical measures such as deviations and errors.

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A colleague claims that he is 90% sure that advertising does not improve sales and in fact, it might even diminish your revenues. Can you reject his null hypothesis? Explain calculating the test statistic and setting up the hypothesis test correctly (H0: β1 ≤ 0)

A colleague claims that he is 90% sure that advertising does not improve sales and in fact, it might even diminish your revenues. Can you reject his null hypothesis? Explain calculating the test statistic and setting up the hypothesis test correctly (H0: β1 ≤ 0)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A colleague claims that he is 90% sure that advertising does not improve sales and in fact, it might even diminish your revenues. Can you reject his null hypothesis? Explain calculating the test statistic and setting up the hypothesis test correctly (H0: β1 ≤ 0)

**Table Title:** Sample Data for Sales (y) and Number of Ads (x)

This table provides data from six advertising campaigns, showing the number of ads (x) and the resulting sales revenues (y). Variables are defined as follows:

- **Obs.:** Observation number
- **x:** Number of ads
- **y:** Sales revenue
- \(x_i - \bar{x}\): Difference between individual x values and the mean of x
- \((x_i - \bar{x})^2\): Square of the deviation of x
- \(y_i - \bar{y}\): Difference between individual y values and the mean of y
- \((x_i - \bar{x})(y_i - \bar{y})\): Product of deviations from the mean for x and y
- \(\hat{y}_i\): Predicted y value
- \(e_i\): Error term (difference between actual and predicted y values)
- \((y_i - \bar{y})^2\): Square of the deviation of y
- \((\hat{y}_i - \bar{y})^2\): Square of the deviation of predicted y

**Observations:**

1. **Observation 1:**
- x = 10, y = 49

2. **Observation 2:**
- x = 6, y = 41

3. **Observation 3:**
- x = 16, y = 49

4. **Observation 4:**
- x = 8, y = 36

5. **Observation 5:**
- x = 12, y = 46

6. **Observation 6:**
- x = 8, y = 43

This table allows analysis of the relationship between the number of ads and sales revenue, incorporating statistical measures such as deviations and errors.

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