Having trouble with this question. Thank you for the help! The image contains a segment of a statistical analysis worksheet, focusing on hypothesis testing and confidence interval calculation. Below is the transcribed content suitable for an educational website:---### Statistical Analysis Worksheet1. **[Section details not fully visible]** 8a) $ H_0 $ _________________ $ H_1 $ _________________ $ z = $ _________________ P-Value = _________________ **Conclusion** _________________ 8b) $ z_{\alpha/2} = $ _________________ $ E = $ _________________ CI: _________________ **Conclusion** _________________ 2. **[Section details not fully visible]** - a) = 0.37 - b) = 40.032---**Explanation of Sections:**- **8a) Hypothesis Testing:** - **$ H_0 $:** This represents the null hypothesis, a statement which indicates no effect or no difference. - **$ H_1 $:** This stands for the alternative hypothesis, indicating some effect or difference. - **$ z $:** The z-score or z-value measures how many standard deviations an element is from the mean. - **P-Value:** The probability value used to determine the significance of the results. A lower p-value indicates stronger evidence against the null hypothesis. - **Conclusion:** Based on the z-value and p-value, a decision is made to either reject or fail to reject the null hypothesis.- **8b) Confidence Interval Calculation:** - **$ z_{\alpha/2} $:** The critical value from the z-distribution for a given confidence level. - **$ E $:** The margin of error in the estimate. - **CI:** The confidence interval, providing a range of values which is expected to contain the population parameter. - **Conclusion:** An interpretation of the confidence interval, typically involves statements about the reliability of the interval and what it suggests about the population parameter.This worksheet segment guides learners through performing hypothesis testing and calculating confidence intervals, essential skills in inferential statistics. ### Investigating the Preference for Chocolate Desserts**Problem Statement:**A survey was conducted to determine the preference for chocolate-containing desserts among men and women. The survey results revealed the following:- Out of 200 men, 98 responded "yes" to liking chocolate in their favorite dessert.- Out of 130 women, 94 said "yes" to the same question.Given a significance level of $\alpha = 0.05$, the goal is to test the claim that the proportion of men who prefer chocolate in their favorite dessert is lower than that of women.**Tasks:****a.) Use a Hypothesis Test** - **Null Hypothesis ($H_0$)**: The proportion of men who prefer chocolate in their favorite dessert is equal to the proportion of women who prefer chocolate in their favorite dessert. \[ H_0: P_m = P_w \] - **Alternative Hypothesis ($H_a$)**: The proportion of men who prefer chocolate in their favorite dessert is lower than the proportion of women who prefer chocolate in their favorite dessert. \[ H_a: P_m < P_w \]**b.) Use a Confidence Interval** Calculate the confidence interval for the difference in proportions to assess whether the proportion of men who prefer chocolate in their favorite dessert is lower than that of women.### Data Summary:- Number of men surveyed ($n_m$): 200- Number of men who said "yes" ($X_m$): 98- Number of women surveyed ($n_w$): 130- Number of women who said "yes" ($X_w$): 94#### Graphs and Diagrams:*No graphs or diagrams were provided in the source material.* This problem can be addressed through statistical analysis using both hypothesis testing and confidence interval calculations to either support or refute the given claim based on the provided data.

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Description: Having trouble with this question. Thank you for the help! The image contains a segment of a statistical analysis worksheet, focusing on hypothesis testing and confidence interval calculation. Below is the transcribed content suitable for an educatio

Given, No. of mean, n1 =200 No. of men said yes, X1 = 98 No. of women,n2 = 130 No. of women said yes…

Math

Statistics

8.) People were asked if their favorite dessert has chocolate in it. Out of 200 men, aid "yes," and out of 130 women, 94 said "yes." At a = 0.05, test the claim that the roportion of men is lower. a.) Use a hypothesis test b.) Use a confidence interval

8.) People were asked if their favorite dessert has chocolate in it. Out of 200 men, aid "yes," and out of 130 women, 94 said "yes." At a = 0.05, test the claim that the roportion of men is lower. a.) Use a hypothesis test b.) Use a confidence interval

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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Concept explainers

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.

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Having trouble with this question. Thank you for the help!

The image contains a segment of a statistical analysis worksheet, focusing on hypothesis testing and confidence interval calculation. Below is the transcribed content suitable for an educational website:

---

### Statistical Analysis Worksheet

1. **[Section details not fully visible]**

8a) $ H_0 $ _________________ $ H_1 $ _________________
$ z = $ _________________ P-Value = _________________
**Conclusion** _________________

8b) $ z_{\alpha/2} = $ _________________ $ E = $ _________________ CI: _________________
**Conclusion** _________________

2. **[Section details not fully visible]**
- a) = 0.37
- b) = 40.032

---

**Explanation of Sections:**

- **8a) Hypothesis Testing:**
- **$ H_0 $:** This represents the null hypothesis, a statement which indicates no effect or no difference.
- **$ H_1 $:** This stands for the alternative hypothesis, indicating some effect or difference.
- **$ z $:** The z-score or z-value measures how many standard deviations an element is from the mean.
- **P-Value:** The probability value used to determine the significance of the results. A lower p-value indicates stronger evidence against the null hypothesis.
- **Conclusion:** Based on the z-value and p-value, a decision is made to either reject or fail to reject the null hypothesis.

- **8b) Confidence Interval Calculation:**
- **$ z_{\alpha/2} $:** The critical value from the z-distribution for a given confidence level.
- **$ E $:** The margin of error in the estimate.
- **CI:** The confidence interval, providing a range of values which is expected to contain the population parameter.
- **Conclusion:** An interpretation of the confidence interval, typically involves statements about the reliability of the interval and what it suggests about the population parameter.

This worksheet segment guides learners through performing hypothesis testing and calculating confidence intervals, essential skills in inferential statistics.

### Investigating the Preference for Chocolate Desserts

**Problem Statement:**

A survey was conducted to determine the preference for chocolate-containing desserts among men and women. The survey results revealed the following:

- Out of 200 men, 98 responded "yes" to liking chocolate in their favorite dessert.
- Out of 130 women, 94 said "yes" to the same question.

Given a significance level of $\alpha = 0.05$, the goal is to test the claim that the proportion of men who prefer chocolate in their favorite dessert is lower than that of women.

**Tasks:**

**a.) Use a Hypothesis Test**

- **Null Hypothesis ($H_0$)**: The proportion of men who prefer chocolate in their favorite dessert is equal to the proportion of women who prefer chocolate in their favorite dessert.
\[ H_0: P_m = P_w \]

- **Alternative Hypothesis ($H_a$)**: The proportion of men who prefer chocolate in their favorite dessert is lower than the proportion of women who prefer chocolate in their favorite dessert.
\[ H_a: P_m < P_w \]

**b.) Use a Confidence Interval**

Calculate the confidence interval for the difference in proportions to assess whether the proportion of men who prefer chocolate in their favorite dessert is lower than that of women.

### Data Summary:

- Number of men surveyed ($n_m$): 200
- Number of men who said "yes" ($X_m$): 98
- Number of women surveyed ($n_w$): 130
- Number of women who said "yes" ($X_w$): 94

#### Graphs and Diagrams:

*No graphs or diagrams were provided in the source material.*

This problem can be addressed through statistical analysis using both hypothesis testing and confidence interval calculations to either support or refute the given claim based on the provided data.

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