According to a food website, the mean consumption of popcorn annually by Americans is 59 quarts. The marketing division of the food website unleashes an aggressive campaign designed to get Americans to consume even more popcorn. Complete parts (a) through (c) below (a) Determine the null and alternative hypotheses that would be used to test the effectiveness of the marketing campaign Ho H 59 H₂ H #59 (Type integers or decimals. Do not round.) (b) A sample of 832 Americans provides enough evidence to conclude that marketing campaign was effective. Provide a statement that should be put out by the marketing department = OA. There is sufficient evidence to conclude that the mean consumption of popcorn has risen B. There is sufficient evidence to conclude that the mean consumption of popcorn has stayed the same. CIT D OC. There is not sufficient evidence to conclude that the mean consumption of popcorn has risen OD. There is not sufficient evidence to conclude that the mean consumption of popcorn has stayed the same. (c) Suppose, in fact, the mean annual consumption of popcorn after the marketing campaign is 59 quarts. Has a Type I or Type Il error been made by the marketing department? If we tested this hypothesis at the a= 0.05 level of significance, what is the probability of committing this error? Select the correct choice below and fill in the answer box within your choice (Type an integer or a decimal. Do not round.) OA. The marketing department committed a Type I error because the marketing department did not reject the alternative hypothesis when the null hypothesis was true. The probability of making a Type I error is OB. The marketing department committed a Type II error because the marketing department did not reject the alternative hypothesis when the null hypothesis was true. The probability of making a Type II error is OC. The marketing department committed a Type Il error because the marketing department rejected the null hypothesis when it was true. The probability of making a Type Il error is D. The marketing department committed a Type I error because the marketing department rejected the null hypothesis when it was true. The probability of making a Type I error is

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question

redo a-c

The text focuses on hypothesis testing regarding popcorn consumption in the context of a marketing campaign. Below is a transcription and explanation of the content:

---

**Context:**
According to a food website, the mean annual consumption of popcorn by Americans is 59 quarts. The marketing division of the food website launches an aggressive campaign to encourage Americans to consume even more popcorn. The following parts (a) through (c) involve analyzing the effectiveness of this campaign.

**(a) Determining Hypotheses:**
The task is to determine the null and alternative hypotheses to test the effectiveness of the marketing campaign.

- Null Hypothesis (\[H_0\]): \( \mu = 59 \)
- Alternative Hypothesis (\[H_1\]): \( \mu \neq 59 \)

*Note: Use integers or decimals. Do not round.*

**(b) Analyzing Sample Data:**
A sample of 832 Americans is used to conclude if the marketing campaign was effective. A statement must be provided for the marketing department:

- **A:** There is sufficient evidence to conclude that the mean consumption of popcorn has risen.
- **B:** There is sufficient evidence to conclude that the mean consumption of popcorn has stayed the same.
- **C:** There is not sufficient evidence to conclude that the mean consumption of popcorn has risen.
- **D:** There is not sufficient evidence to conclude that the mean consumption of popcorn has stayed the same.

**(c) Evaluating Errors:**
Suppose the actual mean annual consumption of popcorn after the campaign is still 59 quarts. Determine if a Type I or Type II error was made by the marketing department. Given a significance level (\[\alpha\]) of 0.05, calculate the probability of the error:

- **A:** Type I Error: The marketing department did not reject the alternative hypothesis when the null hypothesis was true. Probability:
- **B:** Type II Error: The marketing department did not reject the alternative hypothesis when the null hypothesis was true. Probability:
- **C:** Type II Error: The marketing department rejected the null hypothesis when it was true. Probability:
- **D:** Type I Error: The marketing department rejected the null hypothesis when it was true. Probability:

---

**Explanation of Errors:**
- *Type I Error:* Occurs when the null hypothesis is rejected despite being true.
- *Type II Error:* Occurs when the null hypothesis is not rejected despite being false.

The probability boxes
Transcribed Image Text:The text focuses on hypothesis testing regarding popcorn consumption in the context of a marketing campaign. Below is a transcription and explanation of the content: --- **Context:** According to a food website, the mean annual consumption of popcorn by Americans is 59 quarts. The marketing division of the food website launches an aggressive campaign to encourage Americans to consume even more popcorn. The following parts (a) through (c) involve analyzing the effectiveness of this campaign. **(a) Determining Hypotheses:** The task is to determine the null and alternative hypotheses to test the effectiveness of the marketing campaign. - Null Hypothesis (\[H_0\]): \( \mu = 59 \) - Alternative Hypothesis (\[H_1\]): \( \mu \neq 59 \) *Note: Use integers or decimals. Do not round.* **(b) Analyzing Sample Data:** A sample of 832 Americans is used to conclude if the marketing campaign was effective. A statement must be provided for the marketing department: - **A:** There is sufficient evidence to conclude that the mean consumption of popcorn has risen. - **B:** There is sufficient evidence to conclude that the mean consumption of popcorn has stayed the same. - **C:** There is not sufficient evidence to conclude that the mean consumption of popcorn has risen. - **D:** There is not sufficient evidence to conclude that the mean consumption of popcorn has stayed the same. **(c) Evaluating Errors:** Suppose the actual mean annual consumption of popcorn after the campaign is still 59 quarts. Determine if a Type I or Type II error was made by the marketing department. Given a significance level (\[\alpha\]) of 0.05, calculate the probability of the error: - **A:** Type I Error: The marketing department did not reject the alternative hypothesis when the null hypothesis was true. Probability: - **B:** Type II Error: The marketing department did not reject the alternative hypothesis when the null hypothesis was true. Probability: - **C:** Type II Error: The marketing department rejected the null hypothesis when it was true. Probability: - **D:** Type I Error: The marketing department rejected the null hypothesis when it was true. Probability: --- **Explanation of Errors:** - *Type I Error:* Occurs when the null hypothesis is rejected despite being true. - *Type II Error:* Occurs when the null hypothesis is not rejected despite being false. The probability boxes
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 5 images

Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman