Find test value and p-score. **Analysis of Length of Unemployment by Industry**This study investigates whether the duration of unemployment depends on the industry type. Utilizing a random sample from three distinct sectors, a hypothesis test is conducted at a 0.10 significance level to explore any potential relationships.**Observed Data:**| Sector | Less than 5 weeks | 5-14 weeks | 15-26 weeks ||-----------------|------------------|------------|-------------|| Transportation | 84 | 112 | 83 || Information | 50 | 55 | 45 || Financial | 89 | 105 | 114 |**Expected Numbers Calculation:**You are requested to calculate the expected values for each category (round to three decimal places).**Expected Data:**| Sector | Less than 5 weeks | 5-14 weeks | 15-26 weeks ||-----------------|------------------|------------|-------------|| Transportation | | | || Information | | | || Financial | | | |To proceed with the hypothesis test, use the chi-square test for independence to determine if there is any significant association between the length of unemployment and the type of industry. Calculate each expected frequency using the formula for expected value in a contingency table:\[ E = \frac{(Row \ Total \times Column \ Total)}{Grand \ Total}\]Fill in the blank cells with the calculated expected values, rounded to three decimal places, to support the hypothesis testing process.

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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Question

Find test value and p-score.

**Analysis of Length of Unemployment by Industry**

This study investigates whether the duration of unemployment depends on the industry type. Utilizing a random sample from three distinct sectors, a hypothesis test is conducted at a 0.10 significance level to explore any potential relationships.

**Observed Data:**

| Sector | Less than 5 weeks | 5-14 weeks | 15-26 weeks |
|-----------------|------------------|------------|-------------|
| Transportation | 84 | 112 | 83 |
| Information | 50 | 55 | 45 |
| Financial | 89 | 105 | 114 |

**Expected Numbers Calculation:**

You are requested to calculate the expected values for each category (round to three decimal places).

**Expected Data:**

| Sector | Less than 5 weeks | 5-14 weeks | 15-26 weeks |
|-----------------|------------------|------------|-------------|
| Transportation | | | |
| Information | | | |
| Financial | | | |

To proceed with the hypothesis test, use the chi-square test for independence to determine if there is any significant association between the length of unemployment and the type of industry. Calculate each expected frequency using the formula for expected value in a contingency table:

\[
E = \frac{(Row \ Total \times Column \ Total)}{Grand \ Total}
\]

Fill in the blank cells with the calculated expected values, rounded to three decimal places, to support the hypothesis testing process.

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.