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Is the length of time of unemployment related to the type of industry? A random sample of unemployed workers from three different work sectors yielded the following data. Perform a hypothesis test at 0.01 level of significance to determine if there is a relationship. Less than 5 weeks 5-14 weeks 15-26 weeks Transportation 89 114 81 Information 58 70 55 Financial 81 113 112 What are the expected numbers? (round to 3 decimal places) Less than 5 weeks 5-14 weeks 15-26 weeks Transportation Information Financial The hypotheses are Họ: The length of unemployment is independent of the type of industry. HA: The length of unemployment is dependent of the type of industry. (claim) Since a = 0.01 the critical value is 13.277 The test value is: (round to 3 decimal places) The p-value is (round to 3 decimal places) So the decision is to O eject Ho O do not reject Ho Thus the final conclusion is O There is enough evidence to support the claim that the length of unemployment is dependent of the type of industry. O There is not enough evidence to support the claim that the length of unemployment is dependent of the type of industry. O There is not enough evidence to reject the claim that the length of unemployment is dependent of the type of industry. O There is enough evidence to reject the claim that the length of unemployment is dependent of the type of industry.

Is the length of time of unemployment related to the type of industry? A random sample of unemployed workers from three different work sectors yielded the following data. Perform a hypothesis test at 0.01 level of significance to determine if there is a relationship. Less than 5 weeks 5-14 weeks 15-26 weeks Transportation 89 114 81 Information 58 70 55 Financial 81 113 112 What are the expected numbers? (round to 3 decimal places) Less than 5 weeks 5-14 weeks 15-26 weeks Transportation Information Financial The hypotheses are Họ: The length of unemployment is independent of the type of industry. HA: The length of unemployment is dependent of the type of industry. (claim) Since a = 0.01 the critical value is 13.277 The test value is: (round to 3 decimal places) The p-value is (round to 3 decimal places) So the decision is to O eject Ho O do not reject Ho Thus the final conclusion is O There is enough evidence to support the claim that the length of unemployment is dependent of the type of industry. O There is not enough evidence to support the claim that the length of unemployment is dependent of the type of industry. O There is not enough evidence to reject the claim that the length of unemployment is dependent of the type of industry. O There is enough evidence to reject the claim that the length of unemployment is dependent of the type of industry.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Analysis of Unemployment Duration by Industry Type** This exercise investigates whether the length of unemployment is related to the type of industry. Data from a random sample of unemployed workers across three sectors—Transportation, Information, and Financial—are analyzed using a hypothesis test at a 0.01 significance level to determine any possible relationships. **Data Table:** - **Transportation:** Less than 5 weeks (89), 5-14 weeks (114), 15-26 weeks (81) - **Information:** Less than 5 weeks (58), 5-14 weeks (70), 15-26 weeks (55) - **Financial:** Less than 5 weeks (81), 5-14 weeks (113), 15-26 weeks (112) **Expected Numbers Table:** - Calculate expected numbers for each category by rounding to three decimal places. **Hypotheses:** - Null Hypothesis (\(H_0\)): The length of unemployment is independent of the type of industry. - Alternative Hypothesis (\(H_A\)): The length of unemployment is dependent on the type of industry. **Statistical Analysis:** - **Significance Level (\(\alpha\))**: 0.01 with a critical value of 13.277. - **Test Value**: To be calculated and rounded to three decimal places. - **p-value**: To be calculated and rounded to three decimal places. **Decision:** - Choose whether to reject or not reject \(H_0\) based on the test results. **Conclusion:** - Determine whether there is sufficient evidence to support or reject the dependency between unemployment length and industry, considering the given options: - There is enough evidence to support the claim that unemployment duration is industry-dependent. - There is not enough evidence to support dependency. - Insufficient evidence to reject dependency. - Sufficient evidence to reject dependency. This structured approach ensures a thorough understanding of the relationship between unemployment duration and industry type.
Transcribed Image Text:**Analysis of Unemployment Duration by Industry Type** This exercise investigates whether the length of unemployment is related to the type of industry. Data from a random sample of unemployed workers across three sectors—Transportation, Information, and Financial—are analyzed using a hypothesis test at a 0.01 significance level to determine any possible relationships. **Data Table:** - **Transportation:** Less than 5 weeks (89), 5-14 weeks (114), 15-26 weeks (81) - **Information:** Less than 5 weeks (58), 5-14 weeks (70), 15-26 weeks (55) - **Financial:** Less than 5 weeks (81), 5-14 weeks (113), 15-26 weeks (112) **Expected Numbers Table:** - Calculate expected numbers for each category by rounding to three decimal places. **Hypotheses:** - Null Hypothesis (\(H_0\)): The length of unemployment is independent of the type of industry. - Alternative Hypothesis (\(H_A\)): The length of unemployment is dependent on the type of industry. **Statistical Analysis:** - **Significance Level (\(\alpha\))**: 0.01 with a critical value of 13.277. - **Test Value**: To be calculated and rounded to three decimal places. - **p-value**: To be calculated and rounded to three decimal places. **Decision:** - Choose whether to reject or not reject \(H_0\) based on the test results. **Conclusion:** - Determine whether there is sufficient evidence to support or reject the dependency between unemployment length and industry, considering the given options: - There is enough evidence to support the claim that unemployment duration is industry-dependent. - There is not enough evidence to support dependency. - Insufficient evidence to reject dependency. - Sufficient evidence to reject dependency. This structured approach ensures a thorough understanding of the relationship between unemployment duration and industry type.
Expert Solution
Step 1
  Less than 5 Weeks 5-14 weeks 15-26 weeks Total
Transportation 89 114 81 284
Information 58 70 55 183
Financial 81 113 112 306
Total 228 297 248 773
         

Expected value of a cell = Row sub total * Column sub totalGrand total

 

Example ( E(Transportation , less than 5 weeks) = 284*228773= 83.767

 

Similarly for others

 

df = (# rows -1 ) (# column - 1) 

    = (3-1)(3-1) = 4 

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Probability homework question answer, step 1, image 1

 

 

 

 

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