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Provide an appropriate response. Find the standardized test statistic to test the claim that H₁ H2. Assume the two samples are random and independent. = Population statistics: 0₁ = 1.5 and 0₂ = 1.9 Sample statistics: x₁= 29, n₁ = 50 and x2 = 27, n₂ = 60 O 4.2 08.1 06.2 3.8

Provide an appropriate response. Find the standardized test statistic to test the claim that H₁ H2. Assume the two samples are random and independent. = Population statistics: 0₁ = 1.5 and 0₂ = 1.9 Sample statistics: x₁= 29, n₁ = 50 and x2 = 27, n₂ = 60 O 4.2 08.1 06.2 3.8

MATLAB: An Introduction with Applications
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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**Finding the Standardized Test Statistic for Equal Means** **Context:** Suppose we need to determine whether two population means (\(\mu_1\) and \(\mu_2\)) are equal. To test this claim, we use a standardized test statistic, assuming the samples are random and independent. **Given:** - **Population Statistics:** - \(\sigma_1 = 1.5\) - \(\sigma_2 = 1.9\) - **Sample Statistics:** - \(\bar{x}_1 = 29\) - \(n_1 = 50\) - \(\bar{x}_2 = 27\) - \(n_2 = 60\) **Task:** Calculate the standardized test statistic to test the hypothesis that \(\mu_1 = \mu_2\). **Options Provided:** - 4.2 - 8.1 - 6.2 - 3.8 **Explanation for Students:** The standardized test statistic for comparing two means is calculated using the formula for the two-sample z-test: \[ z = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}} \] Plug in the values for calculation, and choose the correct option based on your result.
Transcribed Image Text:**Finding the Standardized Test Statistic for Equal Means** **Context:** Suppose we need to determine whether two population means (\(\mu_1\) and \(\mu_2\)) are equal. To test this claim, we use a standardized test statistic, assuming the samples are random and independent. **Given:** - **Population Statistics:** - \(\sigma_1 = 1.5\) - \(\sigma_2 = 1.9\) - **Sample Statistics:** - \(\bar{x}_1 = 29\) - \(n_1 = 50\) - \(\bar{x}_2 = 27\) - \(n_2 = 60\) **Task:** Calculate the standardized test statistic to test the hypothesis that \(\mu_1 = \mu_2\). **Options Provided:** - 4.2 - 8.1 - 6.2 - 3.8 **Explanation for Students:** The standardized test statistic for comparing two means is calculated using the formula for the two-sample z-test: \[ z = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}} \] Plug in the values for calculation, and choose the correct option based on your result.
Expert Solution
Step 1: Determine the given variables.

The question is about hypothesis testing.

Given :

Randomly selected no. of observations from population 1 ( n1 ) = 50

Mean of the samples that are selected from population 1 ( x with bar on top subscript 1 ) = 29

Standard deviation of the population 1 ( sigma subscript 1 ) = 1.5

Randomly selected no. of observations from population 2 ( n2 ) = 60

Mean of the samples that are selected from population 2 ( x with bar on top subscript 2 ) = 27

Standard deviation of the population 2 ( sigma subscript 2 ) = 1.9


To find :

Test statistic value.

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