## Paired t-Test Hypothesis TestingThe null hypothesis is defined as \(H_0: \mu_1 = \mu_2\) and the alternative hypothesis as \(H_a: \mu_1 > \mu_2\). The provided data come from a simple random paired sample from two populations under consideration. The paired t-test is used to perform the required hypothesis test at the 10% significance level.### Hypotheses- **Null Hypothesis (\(H_0\)):** \(\mu_1 = \mu_2\)- **Alternative Hypothesis (\(H_a\)):** \(\mu_1 > \mu_2\)### DataThe data sets from Population 1 and Population 2 are paired as follows:| Pair | Population 1 | Population 2 ||------|--------------|--------------|| 1 | 24 | 20 || 2 | 9 | 10 || 3 | 20 | 19 || 4 | 13 | 8 || 5 | 8 | 5 || 6 | 14 | 14 || 7 | 10 | 15 || 8 | 22 | 28 |### ProcedureTo conduct the paired t-test, follow these steps:1. Calculate the differences between each pair (Population 1 - Population 2).2. Find the mean (\(\bar{d}\)) and the standard deviation (\(s_d\)) of these differences.3. Determine the test statistic \(t\) using the formula: \[ t = \frac{\bar{d}}{s_d / \sqrt{n}} \] where \(n\) is the number of pairs.4. Compare the calculated \(t\) value to the critical value from the t-distribution table at the 10% significance level.### ObjectiveFind the test statistic \(t\). Use \( \text{Population 1} - \text{Population 2} \) as the difference.\[ t = \_\_\_ \](Round to three decimal places as needed.) ### t-TableThis t-table displays critical values of t at various significance levels for different degrees of freedom (df). The table is essential for conducting t-tests in statistics to determine the significance of sample data. The significance levels provided are 0.10, 0.05, 0.025, 0.01, and 0.005. Below is a detailed breakdown of the table:\[\begin{array}{|c|c|c|c|c|c|c|}\hline\text{df} & t_{0.10} & t_{0.05} & t_{0.025} & t_{0.01} & t_{0.005} & \text{df} \\\hline1 & 3.078 & 6.314 & 12.706 & 31.821 & 63.657 & 1 \\2 & 1.886 & 2.920 & 4.303 & 6.965 & 9.925 & 2 \\3 & 1.638 & 2.353 & 3.182 & 4.541 & 5.841 & 3 \\4 & 1.533 & 2.132 & 2.776 & 3.747 & 4.604 & 4 \\5 & 1.476 & 2.015 & 2.571 & 3.365 & 4.032 & 5 \\6 & 1.440 & 1.943 & 2.447 & 3.143 & 3.707 & 6 \\7 & 1.415 & 1.895 & 2.365 & 2.998 & 3.499 & 7 \\8 & 1.397 & 1.860 & 2.306 & 2.896 & 3.355 & 8 \\9 & 1.383 & 1.833 & 2.262 & 2.821 & 3.250 & 9 \\10 & 1.

Name: ## Paired t-Test Hypothesis TestingThe null hypothesis is defined as
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Description: ## Paired t-Test Hypothesis TestingThe null hypothesis is defined as \(H_0: \mu_1 = \mu_2\) and the alternative hypothesis as \(H_a: \mu_1 > \mu_2\). The provided data come from a simple random paired sample from two populations under consideration.

The formula for computing test statistic for the paired t test is, The formula for computing mean…

Math

Statistics

Họ: H = H2 and the alternative hypothesis is as specified. The provided data are from a simple random paired sample from the two nsideration. Use the paired t-test to perform the required hypothesis test at the 10% significance level. Obse Pair Popula 24 2 9 3 20 13 8 view the t-table. 4. 5 6 7 14 10 22 Use population 1- population 2 as the difference. hal places as needed.)

Họ: H = H2 and the alternative hypothesis is as specified. The provided data are from a simple random paired sample from the two nsideration. Use the paired t-test to perform the required hypothesis test at the 10% significance level. Obse Pair Popula 24 2 9 3 20 13 8 view the t-table. 4. 5 6 7 14 10 22 Use population 1- population 2 as the difference. hal places as needed.)

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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