A market research firm used a sample of individuals to rate the purchase potential of a particular product before and after the individuals saw a new television commercial about the product. The purchase potential ratings were based on a 0 to 10 scale, with higher values indicating a higher purchase potential The null hypothesis stated that the mean rating "after" would be less than or equal to the mean rating "before." Rejection of this hypothesis would show that the commercial improved the mean purchase potential rating. Use a = 0.05 and the following data to test the hypothesis and comment on the value of the commercial. Individual After ⒸHO: MgSO H₂: Hg = 0 Hoi Ha 50 H₂: Hg > 0 1 ⒸHo: Mg = 0 H₂ Họ 2 3 4 5 6 Purchase Rating Before 5 7 8 6 6 7 4 3 9 7 6 4 8 3 7 8 State the null and alternative hypotheses. (Use mean rating after - mean rating before.) Ho: M₂0 Hai Hd=0 5 7 ⒸHO: Hd > 0 H₂: Ha so Calculate the value of the test statistic. (Round your answer to three decimal places.) Calculate the p-value. (Round your answer to four decimal places.) p-value= State your conclusion. O Do not reject Ho. There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. O Reject Ho. There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. O Reject Ho. There is sufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. O Do not Reject Ho. There is sufficient evidence to conclude that seeing the commercial improves the mean potential to purchase.
A market research firm used a sample of individuals to rate the purchase potential of a particular product before and after the individuals saw a new television commercial about the product. The purchase potential ratings were based on a 0 to 10 scale, with higher values indicating a higher purchase potential The null hypothesis stated that the mean rating "after" would be less than or equal to the mean rating "before." Rejection of this hypothesis would show that the commercial improved the mean purchase potential rating. Use a = 0.05 and the following data to test the hypothesis and comment on the value of the commercial. Individual After ⒸHO: MgSO H₂: Hg = 0 Hoi Ha 50 H₂: Hg > 0 1 ⒸHo: Mg = 0 H₂ Họ 2 3 4 5 6 Purchase Rating Before 5 7 8 6 6 7 4 3 9 7 6 4 8 3 7 8 State the null and alternative hypotheses. (Use mean rating after - mean rating before.) Ho: M₂0 Hai Hd=0 5 7 ⒸHO: Hd > 0 H₂: Ha so Calculate the value of the test statistic. (Round your answer to three decimal places.) Calculate the p-value. (Round your answer to four decimal places.) p-value= State your conclusion. O Do not reject Ho. There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. O Reject Ho. There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. O Reject Ho. There is sufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. O Do not Reject Ho. There is sufficient evidence to conclude that seeing the commercial improves the mean potential to purchase.
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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![### Evaluating the Impact of a Television Commercial on Product Purchase Ratings
A market research firm used a sample of individuals to rate the purchase potential of a particular product before and after they were exposed to a new television commercial about the product. The purchase potential ratings were recorded on a scale from 0 to 10, where higher values indicate a higher purchase potential. The null hypothesis posited that the mean rating "after" the commercial would not differ from the mean rating "before" the commercial. Rejection of this hypothesis would suggest that the commercial improved the mean purchase potential rating.
Using a significance level (α) of 0.05, the following data were gathered to test the hypothesis and make conclusions about the value of the commercial:
#### Purchase Ratings (Before and After Watching the Commercial)
| Individual | After | Before |
|------------|-------|--------|
| 1 | 6 | 5 |
| 2 | 6 | 4 |
| 3 | 7 | 8 |
| 4 | 4 | 3 |
| 5 | 3 | 7 |
| 6 | 9 | 8 |
| 7 | 7 | 5 |
| 8 | 6 | 7 |
### Hypothesis Testing Framework
#### Null and Alternative Hypotheses
Use \(\mu_d\) to represent the mean rating after minus the mean rating before.
1. \( \mathbf{H_0: \mu_d = 0} \)
2. \( \mathbf{H_a: \mu_d > 0} \)
#### Calculation Steps
1. **Calculate the test statistic:** (Round your answer to three decimal places.)
2. **Calculate the p-value:** (Round your answer to four decimal places.)
#### p-value Calculation
\[ \text{p-value} = \]
### Conclusions
Based on the results from the test statistic and the p-value, the following conclusions can be drawn:
1. **Do not reject \( H_0 \):** There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase.
2. **Reject \( H_0 \):** There is sufficient evidence to conclude that seeing the commercial improves the mean potential to purchase.
Select the correct conclusion based on the calculated p-value and test statistic.
### Summary](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F928f3826-faea-4936-b5b6-4aab28469498%2F3aab01aa-e36f-4515-a375-a39052aabf3d%2Fe3qchy8_processed.png&w=3840&q=75)
Transcribed Image Text:### Evaluating the Impact of a Television Commercial on Product Purchase Ratings
A market research firm used a sample of individuals to rate the purchase potential of a particular product before and after they were exposed to a new television commercial about the product. The purchase potential ratings were recorded on a scale from 0 to 10, where higher values indicate a higher purchase potential. The null hypothesis posited that the mean rating "after" the commercial would not differ from the mean rating "before" the commercial. Rejection of this hypothesis would suggest that the commercial improved the mean purchase potential rating.
Using a significance level (α) of 0.05, the following data were gathered to test the hypothesis and make conclusions about the value of the commercial:
#### Purchase Ratings (Before and After Watching the Commercial)
| Individual | After | Before |
|------------|-------|--------|
| 1 | 6 | 5 |
| 2 | 6 | 4 |
| 3 | 7 | 8 |
| 4 | 4 | 3 |
| 5 | 3 | 7 |
| 6 | 9 | 8 |
| 7 | 7 | 5 |
| 8 | 6 | 7 |
### Hypothesis Testing Framework
#### Null and Alternative Hypotheses
Use \(\mu_d\) to represent the mean rating after minus the mean rating before.
1. \( \mathbf{H_0: \mu_d = 0} \)
2. \( \mathbf{H_a: \mu_d > 0} \)
#### Calculation Steps
1. **Calculate the test statistic:** (Round your answer to three decimal places.)
2. **Calculate the p-value:** (Round your answer to four decimal places.)
#### p-value Calculation
\[ \text{p-value} = \]
### Conclusions
Based on the results from the test statistic and the p-value, the following conclusions can be drawn:
1. **Do not reject \( H_0 \):** There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase.
2. **Reject \( H_0 \):** There is sufficient evidence to conclude that seeing the commercial improves the mean potential to purchase.
Select the correct conclusion based on the calculated p-value and test statistic.
### Summary
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