9 Is the length of time of unemployment related to the type of industry? A random sample of unemployedworkers from three different work sectors yielded the following data. Perform a hypothesis test at 0.01level of significance to determine if there is a relationship.Less than 5 weeks5-14 weeks15-26 weeksTransportation8011181Information547540Financial81105118What are the expected numbers? (round to 3 decimal places)Less than 5 weeks5-14 weeks15-26 weeksTransportationInformationFinancialThe hypotheses areHo: 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 13.277The test value is:(round to 3 decimal places)The p-value is(round to 3 decimal places)So the decision is toO reject HoO do not reject HoThus the final conclusion isO There is enough evidence to support the claim that the length of unemployment is dependent of thetype of industry.There is not enough evidence to reject the claim that the length of unemployment is dependent ofthe type of industry.O There is enough evidence to reject the claim that the length of unemployment is dependent of thetype of industry.O There is not enough evidence to support the claim that the length of unemployment is dependent ofthe type of industry.

Name: 9 Is the length of time of unemployment related to the type of industr
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Description: 9 Is the length of time of unemployment related to the type of industry? A random sample of unemployedworkers from three different work sectors yielded the following data. Perform a hypothesis test at 0.01level of significance to determine if there i

The row and column totals are, Less than 5 weeks 5-14 weeks 15-26 weeks Total Transportation 80 111 81 272 Information 54 75 40 169 Financial 81 105 118 304 Total 215 291 239 745 The expected numbers are, Less than 5 weeks 5-14 weeks 15-26 weeks Total Transportation 272×215745=78.497 272×291745=106.244 272×239745=87.259 272 Information 169×215745=48.772 169×291745=66.012 169×239745=54.216 169 Financial 304×215745=87.731 304×291745=118.744 304×239745=97.525 304 Total 215 291 239 745The test statistic value is, χ2=Sum ofObserved-Expected2Expected=80-78.497278.497+111-106.2442106.244+81-87.259287.259+54-48.772248.772+75-66.012266.012+40-54.216254.216+81-87.731287.731+105-118.7442118.744+118-97.525297.525=0.029+0.213+0.449+0.560+1.224+3.728+0.517+1.591+4.299=12.608 Thus, the test statistic is 12.608. The degrees of freedom is, df=r-1c-1=3-13-1=4 The degrees of freedom is 4. Computation of p-value: The p-value of χ2-distribution at 4 degrees of freedom can be obtained using the excel formula “=CHISQ.DIST.RT(12.608,4)”. The p-value is 0.013. Thus, the p-value is 0.013. Decision rule: If p-value≤α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis. Conclusion: The p-value (0.013) is greater than the level of significance (0.01). Based on decision rule, do not reject the null hypothesis. Thus, the final conclusion is there is enough evidence to support the claim that the length of unemployment is dependent of the type of industry.

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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 80 111 81 Information 54 75 40 Financial 81 105 118

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 80 111 81 Information 54 75 40 Financial 81 105 118

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

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Question

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
80
111
81
Information
54
75
40
Financial
81
105
118
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
Ho: 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 reject 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.
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.
O There is not enough evidence to support the claim that the length of unemployment is dependent of
the type of industry.

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