nce to determine if there is a relationship. Less than 5 weeks 5-14 weeks tation 84 112 ation 50 55 cial 89 105
Find test value and p-score.
![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 0.10
level of significance to determine if there is a relationship.
Less than 5 weeks
5-14 weeks
15-26 weeks
Transportation
84
112
83
Information
50
55
45
Financial
89
105
114
What are the expected numbers? (round to 3 decimal places)
Less than 5 weeks
5-14 weeks
15-26 weeks
Transportation
Information
Financial](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd42174da-fc06-4bb4-b36e-d78b2115a5c8%2F3019da22-edcc-4cd1-aa88-1229a068bc01%2Flyple7_processed.png&w=3840&q=75)
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Let A and B be the two attributes divided into r and s classes respectively. Then, to test whether the attributes A and B are independent or not, following procedure will be followed:
Let oij is the observed frequency for contingency table category in column i and row j and eij is the corresponding expected frequency for contingency table category in column i and row j.
Null hypothesis: the attributes A and B are independent.
Alternative hypothesis: the attributes A and B are not independent.
Test statistics:
The expected frequency is calculated as . N is total frequency. Here, ri and cj are ith row total and jth column total and follows chi-square distribution with degree of freedom. Now compute the p-value associated with the calculated value at given level of significance and degree of freedom, we will accept or reject the hypothesis.
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