11 ### Hypothesis Testing for Bonus Opportunities: Men vs. Women**Scenario:**A CEO claims that men and women working for his company have equal opportunities to earn bonuses. However, a lawyer representing a female employee argues that men have greater bonus opportunities than women at the company. We will test this claim at a significance level of $\alpha = 0.05$.**Definitions:**- $ p_M $: Proportion of men who have received a bonus in the past year.- $ p_W $: Proportion of women who have received a bonus in the past year.**Hypotheses:**Select the correct hypotheses for this test:- $ H_0: p_M = p_W, \ H_a: p_M > p_W $- $ H_0: p_M \neq p_W, \ H_a: p_M > p_W $- $ H_0: p_M = p_W, \ H_a: p_M \neq p_W $- $ H_0: p_M = p_W, \ H_a: p_M < p_W $**Data:**- From a random sample of 315 men, 287 had received a bonus in the past year.- From a random sample of 232 women, 187 had received a bonus in the past year.**Statistical Analysis:**To proceed, we need to calculate the test statistic and the p-value to determine whether we should reject the null hypothesis.1. **Find the test statistic (rounded to 4 decimal places):** ``` [Input box for test statistic] ```2. **Find the p-value (rounded to 4 decimal places):** ``` [Input box for p-value] ```**Decision:**Based on the computed p-value, select the correct decision:- Reject the Null Hypothesis- Do not Reject the Null HypothesisThis setup guides the user through the hypothesis testing process, providing a structured approach to determine whether there is a statistically significant difference in bonus opportunities between men and women in the company.

Name: 11 ### Hypothesis Testing for Bonus Opportunities: Men vs. Women**Scen
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Description: 11 ### Hypothesis Testing for Bonus Opportunities: Men vs. Women**Scenario:**A CEO claims that men and women working for his company have equal opportunities to earn bonuses. However, a lawyer representing a female employee argues that men have great

We have given that Sample size N1=315 ,N2=232 And Favorable cases X1=287, X2=187 Alpha =0.05

Math

Statistics

A CEO claims that men and women working for his company have equal opportunities to earn bonuses. A lawyer working on a lawsuit filed by a female employee claims that men have greater bonus opportunities than women working at the company. Test this claim at the a = 0.05 level of significance. Let pM represent the proportion of men working for the company that have received a bonus in the past year and Pw represent the proportion of women working for the company that have received a bonus in the past year. Select the correct hypotheses for this test: Ho:PM —D Рw, Hа:pм > Рw Но: рм 7 рw, Ha: рм > рw Но: рм — ри, Ha:рм # pw О Но: рм — pw, Ha:рм < pw In a random sample of 315 men, 287 had received a bonus in the past year. In a random sample of 232 women, 187 had received a bonus in the past year. Find the test statistic (round to 4 decimal places): Find the p-value (round to 4 decimal places): Select the correct decision: O Reject the Null Hypothesis O Do not Reject the Null Hypothesis

A CEO claims that men and women working for his company have equal opportunities to earn bonuses. A lawyer working on a lawsuit filed by a female employee claims that men have greater bonus opportunities than women working at the company. Test this claim at the a = 0.05 level of significance. Let pM represent the proportion of men working for the company that have received a bonus in the past year and Pw represent the proportion of women working for the company that have received a bonus in the past year. Select the correct hypotheses for this test: Ho:PM —D Рw, Hа:pм > Рw Но: рм 7 рw, Ha: рм > рw Но: рм — ри, Ha:рм # pw О Но: рм — pw, Ha:рм < pw In a random sample of 315 men, 287 had received a bonus in the past year. In a random sample of 232 women, 187 had received a bonus in the past year. Find the test statistic (round to 4 decimal places): Find the p-value (round to 4 decimal places): Select the correct decision: O Reject the Null Hypothesis O Do not Reject the Null Hypothesis

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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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

### Hypothesis Testing for Bonus Opportunities: Men vs. Women

**Scenario:**
A CEO claims that men and women working for his company have equal opportunities to earn bonuses. However, a lawyer representing a female employee argues that men have greater bonus opportunities than women at the company. We will test this claim at a significance level of $\alpha = 0.05$.

**Definitions:**
- $ p_M $: Proportion of men who have received a bonus in the past year.
- $ p_W $: Proportion of women who have received a bonus in the past year.

**Hypotheses:**

Select the correct hypotheses for this test:

- $ H_0: p_M = p_W, \ H_a: p_M > p_W $
- $ H_0: p_M \neq p_W, \ H_a: p_M > p_W $
- $ H_0: p_M = p_W, \ H_a: p_M \neq p_W $
- $ H_0: p_M = p_W, \ H_a: p_M < p_W $

**Data:**

- From a random sample of 315 men, 287 had received a bonus in the past year.
- From a random sample of 232 women, 187 had received a bonus in the past year.

**Statistical Analysis:**

To proceed, we need to calculate the test statistic and the p-value to determine whether we should reject the null hypothesis.

1. **Find the test statistic (rounded to 4 decimal places):**
```
[Input box for test statistic]
```

2. **Find the p-value (rounded to 4 decimal places):**
```
[Input box for p-value]
```

**Decision:**

Based on the computed p-value, select the correct decision:

- Reject the Null Hypothesis
- Do not Reject the Null Hypothesis

This setup guides the user through the hypothesis testing process, providing a structured approach to determine whether there is a statistically significant difference in bonus opportunities between men and women in the company.

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