The first box options are "not in" or "in". Second box is "reject" or "fail to reject" third is "is" or "is not". next sentence first box is "included" or "not". Second box is "reject" or "fail to reject".third sentence first box is "different" or "the same" second box is <,>,= etc. & third box is the same options **Title:** Hypothesis Testing and Confidence Intervals**Overview:**In this example, two different simple random samples are drawn from two different populations. The aim is to compare the results from a hypothesis test of $ p_1 = p_2 $ with a 0.05 significance level and a 95% confidence interval estimate of $ p_1 - p_2 $.- **First Sample:** - Consists of 30 people with 15 having a common attribute. - **Second Sample:** - Consists of 1900 people with 1349 having the same common attribute.**Steps to Complete:**1. **Identify the Test Statistic:** Fill in the blank for the test statistic value rounded to two decimal places as needed.2. **Identify the Critical Value(s):** Determine the critical values by rounding to three decimal places as needed. Use a comma to separate answers if necessary.3. **Conclusion Based on the Hypothesis Test:** - **Decision Rule:** - Compare the test statistic to the critical region. - Decide whether to retain or reject the null hypothesis. - Determine if there is enough evidence to conclude that $ p_1 \neq p_2 $.4. **95% Confidence Interval:** - Compute the confidence interval, rounded to three decimal places, to estimate $ (p_1 - p_2) $.5. **Conclusion Based on the Confidence Interval:** - **Interpretation:** - If 0 is (or is not) in the interval, indicate the implication for the null hypothesis.6. **Comparing Hypothesis Test Results and Confidence Interval:** - Compare the outcomes from the hypothesis test and the confidence interval. - Analyze if the results are consistent, and cross-check the implications for $ p_1 $ and $ p_2 $.**Graphical Analysis (if applicable):**- There are check boxes for different hypothesis test options: - $ H_0: p_1 = p_2 $ - $ H_0: p_1 \geq p_2 $ - $ H_0: p_1 \leq p_2 $- The alternative hypotheses $ H_1 $ have similar completion checkboxes as above.This instructional text guides users through conducting a hypothesis test and understanding how to interpret confidence intervals in statistical **Title:** Hypothesis Testing with Two Populations**Description:**Two different simple random samples are drawn from two different populations. The first sample consists of 30 people with 15 having a common attribute. The second sample consists of 1900 people with 1349 of them having the same common attribute. Compare the results from a hypothesis test of $ p_1 \ne p_2 $ (with a 0.05 significance level) and a 95% confidence interval estimate of $ p_1 - p_2 $.**What are the null and alternative hypotheses for the hypothesis test?**- **Option A:** $ H_0: p_1 \ge p_2 $ $ H_1: p_1 < p_2 $- **Option B:** $ H_0: p_1 \le p_2 $ $ H_1: p_1 \ne p_2 $- **Option C:** $ H_0: p_1 = p_2 $ $ H_1: p_1 \ne p_2 $- **Option D:** $ H_0: p_1 > p_2 $ $ H_1: p_1 \le p_2 $- **Option E:** $ H_0: p_1 \ne p_2 $ $ H_1: p_1 = p_2 $- **Option F:** $ H_0: p_1 = p_2 $ $ H_1: p_1 > p_2 $**Identify the test statistic.**[Input Box] (Round to two decimal places as needed.)**Identify the critical value(s).**[Input Box] (Round to three decimal places as needed. Use a comma to separate answers as needed.)**What is the conclusion based on the hypothesis test?**The test statistic is [Input Box] the critical region, so [Input Box] the null hypothesis. There is [Input Box] evidence to conclude that $ p_1 \ne p_2 $.**The 95% confidence interval is $ [\_\_\_, \_\_\_] $.**(Round to three decimal places as needed.)**What is the conclusion based on the confidence interval

Given : x1= 15 n1= 30 x2= 1349 n2= 1900 significance level, 0.05

Two different simple random samples are drawn from two different populations. The first sample consists of 30 people with 15 having a common attribute. The second sample consists of 1900 people with 1349 of them having the san attribute. Compare the results from a hypothesis test of p, =P2 (with a 0.05 significance level) and a 95% confidence interval estimate of p, -P2 What are the null and altemative hypotheses for the hypothesis test? O A. Ho: P, 2p2 H: P P2 O B. Ho: P1 SP2 H: P P2 O C. Ho: P "pz H P.

Two different simple random samples are drawn from two different populations. The first sample consists of 30 people with 15 having a common attribute. The second sample consists of 1900 people with 1349 of them having the san attribute. Compare the results from a hypothesis test of p, =P2 (with a 0.05 significance level) and a 95% confidence interval estimate of p, -P2 What are the null and altemative hypotheses for the hypothesis test? O A. Ho: P, 2p2 H: P P2 O B. Ho: P1 SP2 H: P P2 O C. Ho: P "pz H P.

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

The first box options are "not in" or "in". Second box is "reject" or "fail to reject" third is "is" or "is not".

next sentence first box is "included" or "not". Second box is "reject" or "fail to reject".

third sentence first box is "different" or "the same" second box is <,>,= etc. & third box is the same options

**Title:** Hypothesis Testing and Confidence Intervals

**Overview:**

In this example, two different simple random samples are drawn from two different populations. The aim is to compare the results from a hypothesis test of $ p_1 = p_2 $ with a 0.05 significance level and a 95% confidence interval estimate of $ p_1 - p_2 $.

- **First Sample:**
- Consists of 30 people with 15 having a common attribute.

- **Second Sample:**
- Consists of 1900 people with 1349 having the same common attribute.

**Steps to Complete:**

1. **Identify the Test Statistic:**

Fill in the blank for the test statistic value rounded to two decimal places as needed.

2. **Identify the Critical Value(s):**

Determine the critical values by rounding to three decimal places as needed. Use a comma to separate answers if necessary.

3. **Conclusion Based on the Hypothesis Test:**

- **Decision Rule:**
- Compare the test statistic to the critical region.
- Decide whether to retain or reject the null hypothesis.
- Determine if there is enough evidence to conclude that $ p_1 \neq p_2 $.

4. **95% Confidence Interval:**

- Compute the confidence interval, rounded to three decimal places, to estimate $ (p_1 - p_2) $.

5. **Conclusion Based on the Confidence Interval:**

- **Interpretation:**
- If 0 is (or is not) in the interval, indicate the implication for the null hypothesis.

6. **Comparing Hypothesis Test Results and Confidence Interval:**

- Compare the outcomes from the hypothesis test and the confidence interval.
- Analyze if the results are consistent, and cross-check the implications for $ p_1 $ and $ p_2 $.

**Graphical Analysis (if applicable):**

- There are check boxes for different hypothesis test options:
- $ H_0: p_1 = p_2 $
- $ H_0: p_1 \geq p_2 $
- $ H_0: p_1 \leq p_2 $
- The alternative hypotheses $ H_1 $ have similar completion checkboxes as above.

This instructional text guides users through conducting a hypothesis test and understanding how to interpret confidence intervals in statistical

**Title:** Hypothesis Testing with Two Populations

**Description:**

Two different simple random samples are drawn from two different populations. The first sample consists of 30 people with 15 having a common attribute. The second sample consists of 1900 people with 1349 of them having the same common attribute. Compare the results from a hypothesis test of $ p_1 \ne p_2 $ (with a 0.05 significance level) and a 95% confidence interval estimate of $ p_1 - p_2 $.

**What are the null and alternative hypotheses for the hypothesis test?**

- **Option A:**
$ H_0: p_1 \ge p_2 $
$ H_1: p_1 < p_2 $

- **Option B:**
$ H_0: p_1 \le p_2 $
$ H_1: p_1 \ne p_2 $

- **Option C:**
$ H_0: p_1 = p_2 $
$ H_1: p_1 \ne p_2 $

- **Option D:**
$ H_0: p_1 > p_2 $
$ H_1: p_1 \le p_2 $

- **Option E:**
$ H_0: p_1 \ne p_2 $
$ H_1: p_1 = p_2 $

- **Option F:**
$ H_0: p_1 = p_2 $
$ H_1: p_1 > p_2 $

**Identify the test statistic.**

[Input Box]
(Round to two decimal places as needed.)

**Identify the critical value(s).**

[Input Box]
(Round to three decimal places as needed. Use a comma to separate answers as needed.)

**What is the conclusion based on the hypothesis test?**

The test statistic is [Input Box] the critical region, so [Input Box] the null hypothesis. There is [Input Box] evidence to conclude that $ p_1 \ne p_2 $.

**The 95% confidence interval is $ [\_\_\_, \_\_\_] $.**

(Round to three decimal places as needed.)

**What is the conclusion based on the confidence interval

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