(a) Determine the null and alternative hypotheses that would be used to test the effectiveness of the marketing campaign. Ho: H,: (Type integers or decimals. Do not round.) (b) A sample of 834 Americans provides enough evidence to conclude that marketing campaign was effective. Provide a statement that should be put out by the marketing department. O A. There is not sufficient evidence to conclude that the mean consumption of popcorn has risen. O B. There is sufficient evidence to conclude that the mean consumption of popcorn has risen. OC. There is not sufficient evidence to conclude that the mean consumption of popcorn has stayed the same. O D. There is 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 61 quarts. Has a Type I or Type Il error been made by the marketing department? If we tested this hypothesis at the a = 0.01 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.) O A. 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 O B. The marketing department committed a Type Il error because the marketing department did not reject the alternative hypothesis when the null hypothesis was true. The probability of making a Type Il error is O C. 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 O 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
(a) Determine the null and alternative hypotheses that would be used to test the effectiveness of the marketing campaign. Ho: H,: (Type integers or decimals. Do not round.) (b) A sample of 834 Americans provides enough evidence to conclude that marketing campaign was effective. Provide a statement that should be put out by the marketing department. O A. There is not sufficient evidence to conclude that the mean consumption of popcorn has risen. O B. There is sufficient evidence to conclude that the mean consumption of popcorn has risen. OC. There is not sufficient evidence to conclude that the mean consumption of popcorn has stayed the same. O D. There is 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 61 quarts. Has a Type I or Type Il error been made by the marketing department? If we tested this hypothesis at the a = 0.01 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.) O A. 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 O B. The marketing department committed a Type Il error because the marketing department did not reject the alternative hypothesis when the null hypothesis was true. The probability of making a Type Il error is O C. 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 O 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
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![**Educational Resource: Analyzing Hypotheses and Errors in Marketing Campaigns**
---
According to a food website, the mean consumption of popcorn annually by Americans is 61 quarts. The marketing division of the food website launches an aggressive campaign designed to encourage more popcorn consumption. Complete the analysis by examining parts (a) through (c) below:
### (a) Hypothesis Testing
**Determine the null and alternative hypotheses to assess the effectiveness of the marketing campaign:**
- **Null Hypothesis (H₀):** The mean annual consumption of popcorn remains 61 quarts.
- **Alternative Hypothesis (H₁):** The mean annual consumption of popcorn is greater than 61 quarts.
*(Note: Type integers or decimals. Do not round.)*
### (b) Evidence from Sample Data
A sample of 834 Americans provides enough evidence to evaluate the effectiveness of the marketing campaign. Choose the appropriate statement to reflect the outcome:
- **A.** There is not 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 risen.
- **C.** There is not sufficient evidence to conclude that the mean consumption of popcorn has stayed the same.
- **D.** There is sufficient evidence to conclude that the mean consumption of popcorn has stayed the same.
### (c) Error Analysis
Suppose, in reality, the mean annual consumption of popcorn after the marketing campaign is still 61 quarts. Determine if a Type I or Type II error was made by the marketing department. Evaluate this within the context of a hypothesis test at the α = 0.01 level of significance. Select the correct choice and calculate the probability of making the specified error:
- **A.** A Type I error was made because the marketing department did not reject the null hypothesis when it was true. *Probability of Type I error is:* [ ]
- **B.** A Type II error was made because the marketing department did not reject the alternative hypothesis when the null hypothesis was true. *Probability of Type II error is:* [ ]
- **C.** A Type II error was made because the marketing department rejected the null hypothesis when it was true. *Probability of Type II error is:* [ ]
- **D.** A Type I error was made because the marketing department rejected the null hypothesis when it was true. *Probability of Type I](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd80315fc-9ba3-472b-8f03-e8ddf0a99e1b%2Fe409b1d3-392a-4df8-a2c8-b0b205543731%2Fiin7mss_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Resource: Analyzing Hypotheses and Errors in Marketing Campaigns**
---
According to a food website, the mean consumption of popcorn annually by Americans is 61 quarts. The marketing division of the food website launches an aggressive campaign designed to encourage more popcorn consumption. Complete the analysis by examining parts (a) through (c) below:
### (a) Hypothesis Testing
**Determine the null and alternative hypotheses to assess the effectiveness of the marketing campaign:**
- **Null Hypothesis (H₀):** The mean annual consumption of popcorn remains 61 quarts.
- **Alternative Hypothesis (H₁):** The mean annual consumption of popcorn is greater than 61 quarts.
*(Note: Type integers or decimals. Do not round.)*
### (b) Evidence from Sample Data
A sample of 834 Americans provides enough evidence to evaluate the effectiveness of the marketing campaign. Choose the appropriate statement to reflect the outcome:
- **A.** There is not 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 risen.
- **C.** There is not sufficient evidence to conclude that the mean consumption of popcorn has stayed the same.
- **D.** There is sufficient evidence to conclude that the mean consumption of popcorn has stayed the same.
### (c) Error Analysis
Suppose, in reality, the mean annual consumption of popcorn after the marketing campaign is still 61 quarts. Determine if a Type I or Type II error was made by the marketing department. Evaluate this within the context of a hypothesis test at the α = 0.01 level of significance. Select the correct choice and calculate the probability of making the specified error:
- **A.** A Type I error was made because the marketing department did not reject the null hypothesis when it was true. *Probability of Type I error is:* [ ]
- **B.** A Type II error was made because the marketing department did not reject the alternative hypothesis when the null hypothesis was true. *Probability of Type II error is:* [ ]
- **C.** A Type II error was made because the marketing department rejected the null hypothesis when it was true. *Probability of Type II error is:* [ ]
- **D.** A Type I error was made because the marketing department rejected the null hypothesis when it was true. *Probability of Type I
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