Last year, 43% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 30% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners. (a) How many business owners in the survey plan to provide a holiday gift to their employees this year? business owners (b) Suppose the business owners in the sample did as they plan. Compute the p-value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = (c) Using a 0.05 level of significance, would you conclude that the proportion of business owners providing gifts decreased? Do not reject Ho. There is sufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year. Do not reject Ho. There is insufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year. Reject Ho. There is sufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year. Reject Ho. There is insufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year. What is the smallest level of significance for which you could draw such conclusion? (Round your answer to four decimal places.)
Last year, 43% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 30% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners. (a) How many business owners in the survey plan to provide a holiday gift to their employees this year? business owners (b) Suppose the business owners in the sample did as they plan. Compute the p-value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = (c) Using a 0.05 level of significance, would you conclude that the proportion of business owners providing gifts decreased? Do not reject Ho. There is sufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year. Do not reject Ho. There is insufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year. Reject Ho. There is sufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year. Reject Ho. There is insufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year. What is the smallest level of significance for which you could draw such conclusion? (Round your answer to four decimal places.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Analysis of Business Owners Giving Holiday Gifts**
*Context:*
Last year, 43% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 30% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners.
---
**(a) Determining the Number of Business Owners Planning to Provide Holiday Gifts This Year**
*Question*:
How many business owners in the survey plan to provide a holiday gift to their employees this year?
*Calculation*:
\[ \text{Number of business owners} = 0.30 \times 60 = 18 \]
---
**(b) Hypothesis Testing for Change in Proportion**
*Procedure*:
Suppose the business owners in the sample did as they plan. Compute the p-value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year.
1. *Find the value of the test statistic.*
\[ \text{(Round your answer to two decimal places.)} \]
*Test Statistic Calculation*:
2. *Find the p-value.*
\[ \text{p-value} = \ \ \ \ \ \ \ (Round your answer to four decimal places.) \]
---
**(c) Conclusion Based on the Level of Significance**
*Question*:
Using a 0.05 level of significance, would you conclude that the proportion of business owners providing gifts decreased?
*Options*:
- Do not reject \( H_0 \): There is sufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year.
- Do not reject \( H_0 \): There is insufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year.
- Reject \( H_0 \): There is sufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year.
- Reject \( H_0 \): There is insufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year.
*Question*:
What is the smallest level of significance for which you could draw such a conclusion?
\[ \text{(Round your answer to four decimal places)} \]
---
**Interactive Help**:
If you need further assistance in understanding the concepts or calculations, click the "Read It" button.
*End of Document*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4ed8498-f2f2-4dcb-bcb0-3b3cd025dd21%2Fb9a3028a-d59f-48ce-92e0-cf555049d3ea%2Fmn0ozcs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Analysis of Business Owners Giving Holiday Gifts**
*Context:*
Last year, 43% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 30% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners.
---
**(a) Determining the Number of Business Owners Planning to Provide Holiday Gifts This Year**
*Question*:
How many business owners in the survey plan to provide a holiday gift to their employees this year?
*Calculation*:
\[ \text{Number of business owners} = 0.30 \times 60 = 18 \]
---
**(b) Hypothesis Testing for Change in Proportion**
*Procedure*:
Suppose the business owners in the sample did as they plan. Compute the p-value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year.
1. *Find the value of the test statistic.*
\[ \text{(Round your answer to two decimal places.)} \]
*Test Statistic Calculation*:
2. *Find the p-value.*
\[ \text{p-value} = \ \ \ \ \ \ \ (Round your answer to four decimal places.) \]
---
**(c) Conclusion Based on the Level of Significance**
*Question*:
Using a 0.05 level of significance, would you conclude that the proportion of business owners providing gifts decreased?
*Options*:
- Do not reject \( H_0 \): There is sufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year.
- Do not reject \( H_0 \): There is insufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year.
- Reject \( H_0 \): There is sufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year.
- Reject \( H_0 \): There is insufficient evidence to conclude that the proportion of business owners providing holiday gifts has decreased from last year.
*Question*:
What is the smallest level of significance for which you could draw such a conclusion?
\[ \text{(Round your answer to four decimal places)} \]
---
**Interactive Help**:
If you need further assistance in understanding the concepts or calculations, click the "Read It" button.
*End of Document*
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