Last year, 41% of business owners gave a holiday gift to their employees. A survey of business owners conducted this vear indicates that 35% planned to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 50 business owners. a. How many business owners the survey planned to provide a holiday gift to their employees this year? Round your answer to the nearest whole number. b. Suppose the business owners in the sample do as they plan. Conduct a hypothesis test that can be used to determine whether the proportion of business owners providing holiday gifts had decreased from last year. State the hypotheses. Họ :P- Select your answer- 0.41 H:p - Select your answer- v0.41 Compute the test statistic and p-value. z-value (to 2 decimals) p-value (to 4 decimals) c. Using a 0.02 level of significance, would you conclude that the proportion of business owners providing gifts decreased? Select your answer- v He. We - Select your answer- v concdude that the proportion business owners providing gifts has decreased from last year to this year. What is the smallest level of significance for whích you could draw such a condusion? (to 4 decimals)
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![**Educational Website Content: Hypothesis Testing in Business Surveys**
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**Context:**
Last year, 41% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 35% planned to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 50 business owners.
**a. Calculation:**
- **Task**: Determine how many business owners in the survey planned to provide a holiday gift to their employees this year. Round your answer to the nearest whole number.
**b. Hypothesis Testing:**
- **Objective**: Conduct a hypothesis test to check if the proportion of business owners providing holiday gifts has decreased from last year.
- **State the Hypotheses:**
- Null Hypothesis (\( H_0 \)): \( p = 0.41 \)
- Alternative Hypothesis (\( H_a \)): \( p < 0.41 \)
- **Compute the Test Statistic and p-value:**
- **z-value**: [Enter value to 2 decimal places]
- **p-value**: [Enter value to 4 decimal places]
**c. Conclusion:**
- **Task**: Using a 0.02 level of significance, decide if the proportion of business owners providing gifts decreased.
- **Conclusion**:
- [Select your answer] \( H_0 \). We [Select your answer] conclude that the proportion of business owners providing gifts has decreased from last year to this year.
- **Further Inquiry**:
- **Smallest Level of Significance**: What is the smallest level of significance for which you could draw such a conclusion?
- [Enter value to 4 decimals]
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This exercise guides users through hypothesis testing, calculation of test statistics, and interpretation of results in the context of business owner practices over two consecutive years.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e8cdcde-da7c-4c36-8088-8e2483af5dc7%2F1bfed152-dddb-4b03-b0f3-bf04cf6ee8fa%2Fo4q11qt_processed.jpeg&w=3840&q=75)
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