### Hypothesis TestingConsider the following hypothesis test:- Null Hypothesis (H₀): μ₁ - μ₂ ≤ 0- Alternative Hypothesis (Hₐ): μ₁ - μ₂ > 0The following results are for two independent samples taken from two populations:#### Sample 1- $ n_1 = 40 $- $ \bar{x}_1 = 25.2 $- $ \sigma_1 = 5.2 $#### Sample 2- $ n_2 = 70 $- $ \bar{x}_2 = 22.9 $- $ \sigma_2 = 7 $### Questions**a.** What is the value of the test statistic (round to 2 decimals)? [Answer Box]**b.** What is the p-value (round to 4 decimals)? Use the z-table. Use z-value rounded to 2 decimal places. [Answer Box]**c.** With $ \alpha = .05 $, what is your hypothesis testing conclusion? p-value is [Drop-down Selection] $ H_0 $ **Consider the following results for two independent random samples taken from two populations.**### Sample 1- $ n_1 = 50 $- $ \bar{x}_1 = 13.9 $- $ \sigma_1 = 2.4 $### Sample 2- $ n_2 = 30 $- $ \bar{x}_2 = 11.2 $- $ \sigma_2 = 3.5 $**a. What is the point estimate of the difference between the two population means? (to 1 decimal)**[Answer Box]**b. Provide a 90% confidence interval for the difference between the two population means (to 2 decimals). Use a z-table.**([Answer Box], [Answer Box])**c. Provide a 95% confidence interval for the difference between the two population means (to 2 decimals). Use a z-table. If your answer is negative, enter minus (-) sign.**([Answer Box], [Answer Box])

Given Information: Null Hypothesis: H0:μ1-μ2≤0 Alternative Hypothesis: Ha:μ1-μ2>0 Sample 1:…

Consider the following hypothesis test. Ho: µ 1 - µ 2 < 0 Hạ: µ 1 - µ 2 > 0 he following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n 1 = 40 n 2 = 70 X 1 = 25.2 X 2 = 22.9 0 1 = 5.2 0 2 = 7 1. What is the value of the test statistic (round to 2 decimals)?

Consider the following hypothesis test. Ho: µ 1 - µ 2 < 0 Hạ: µ 1 - µ 2 > 0 he following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n 1 = 40 n 2 = 70 X 1 = 25.2 X 2 = 22.9 0 1 = 5.2 0 2 = 7 1. What is the value of the test statistic (round to 2 decimals)?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Concept explainers

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

Question

### Hypothesis Testing

Consider the following hypothesis test:

- Null Hypothesis (H₀): μ₁ - μ₂ ≤ 0
- Alternative Hypothesis (Hₐ): μ₁ - μ₂ > 0

The following results are for two independent samples taken from two populations:

#### Sample 1
- $ n_1 = 40 $
- $ \bar{x}_1 = 25.2 $
- $ \sigma_1 = 5.2 $

#### Sample 2
- $ n_2 = 70 $
- $ \bar{x}_2 = 22.9 $
- $ \sigma_2 = 7 $

### Questions

**a.** What is the value of the test statistic (round to 2 decimals)?
[Answer Box]

**b.** What is the p-value (round to 4 decimals)? Use the z-table. Use z-value rounded to 2 decimal places.
[Answer Box]

**c.** With $ \alpha = .05 $, what is your hypothesis testing conclusion?
p-value is [Drop-down Selection] $ H_0 $

**Consider the following results for two independent random samples taken from two populations.**

### Sample 1
- $ n_1 = 50 $
- $ \bar{x}_1 = 13.9 $
- $ \sigma_1 = 2.4 $

### Sample 2
- $ n_2 = 30 $
- $ \bar{x}_2 = 11.2 $
- $ \sigma_2 = 3.5 $

**a. What is the point estimate of the difference between the two population means? (to 1 decimal)**

[Answer Box]

**b. Provide a 90% confidence interval for the difference between the two population means (to 2 decimals). Use a z-table.**

([Answer Box], [Answer Box])

**c. Provide a 95% confidence interval for the difference between the two population means (to 2 decimals). Use a z-table. If your answer is negative, enter minus (-) sign.**

([Answer Box], [Answer Box])

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