Find test value and p-score. 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 0.10level of significance to determine if there is a relationship.Less than 5 weeks5-14 weeks15-26 weeksTransportation8411283Information505545Financial89105114What are the expected numbers? (round to 3 decimal places)Less than 5 weeks5-14 weeks15-26 weeksTransportationInformationFinancial

Answered: nce to determine if there is a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Related questions

Question

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

Expert Solution

Step 1

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 o_ij is the observed frequency for contingency table category in column i and row j and e_ij 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: $χ^{2} = \sum_{i = 1}^{r} \sum_{j = 1}^{s} \frac{{(o_{i j} - e_{i j})}^{2}}{e_{i j}}$

The expected frequency is calculated as $e i j = \frac{r_{i} \times c_{j}}{N}$ . N is total frequency. Here, r_i and c_j are i^throw total and j^thcolumn total and $χ^{2}$ follows chi-square distribution with $(r - 1) (s - 1)$ degree of freedom. Now compute the p-value associated with the calculated $χ^{2}$ value at given level of significance and degree of freedom, we will accept or reject the hypothesis.