**Title: Statistical Analysis of Independent Samples****Introduction**In this lesson, we will explore how to calculate the test statistic for comparing variances of two independent samples. This scenario commonly arises when analyzing data from two different populations to determine if they have different variances.**Problem Statement**Assume that both samples are independent simple random samples from populations having normal distributions.**Task**Use the summary statistics below to find only the test statistic to test the claim that the samples come from populations with different variances. Do not conduct the hypothesis testing.**Summary Statistics**- **Sample A** - \( n = 28 \) (Sample size) - \( \bar{x}_1 = 19.2 \) (Sample mean) - \( s_1 = 4.5 \) (Sample standard deviation)- **Sample B** - \( n = 41 \) (Sample size) - \( \bar{x}_2 = 23.7 \) (Sample mean) - \( s_2 = 5.13 \) (Sample standard deviation)**Objective**To determine the test statistic that helps in assessing whether these two samples come from populations with different variances.**Note**The calculation of the test statistics for comparing variances is typically done using the F-test formula, but for this task, we are focused only on finding this statistic without performing hypothesis testing.By employing these steps, students can confidently calculate the test statistic necessary for comparing two independent sample variances.

4) The sample variance for sample A is 4.5 and the sample variance for sample B is 5.13.

Answered: Assume that both samples are…

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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An HR Director wants to know if there is a difference between Dept 1 and Dept 2 in their employee performance evaluation ratings. The performance evaluation scores for the two departments are below. Perform a t-Test on the data to answer the Director’s question. What is the Null Hypothesis (Ho:)? What is the Research Question or Alternative Hypothesis (Ha:)? Perform the t-Test and show the results (two-sample assume equal variance). Dept 1 Dept 2 3.15 3.2 3.1 3.25 2.95 3.1 3.2 3.6 3.4 2.9 3.12 2.8 3.6 3.1 2.5 3.5 2.8 3.4 2.75 2.8 2.1 2.7 3 3.7 3.2 3.2 3.5 3.5 3.8 3.2 3.2 2.8 3.4 2.15 3.2 2.9 2.6 3.16 2.8 3.14
One sample has n=7 and SS=35 and a second sample has n =17 and SS =45. What is the pooled variance for these two samples?
A researcher takes sample temperatures in Fahrenheit of 17 days from New York City and 18 days from Phoenix. Test the claim that the mean temperature in New York City is different from the mean temperature in Phoenix. Use a significance level of α=0.05. Assume the populations are approximately normally distributed with unequal variances. You obtain the following two samples of data. New York City Phoenix 99 94.2 95.5 72 93.2 86.8 102 122.1 85.4 114.4 80 94.7 86.4 89.7 75.4 104.7 79.5 77.6 83.4 106.8 64.3 98.6 65.5 91.5 87.7 82 104 97.7 74.3 64.9 59.5 82 82.8 72 116.2 The Hypotheses for this problem are: H0: μ1 = μ2 H1: μ1μ2 Find the p-value. Round answer to 4 decimal places. Make sure you put the 0 in front of the decimal. p-value =
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Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. A researcher was interested in comparing the GPAs of students at two different colleges. Independent simple random samples of 8 students from college A and 13 students from college B yielded the following GPAs. College A 3.7 3.2 3.0 2.5 2.7 3.6 2.8 3.4 College B 3.8 3.2 3.0 3.9 3.8 2.5 3.9 2.8 4.0 3.6 2.6 4.0 3.6 Construct a 95% confidence interval for μ1−μ2, the difference between the mean GPA of college A students and the mean GPA of college B students. Round to two decimal places. (Note: x1=3.1125, x2=3.4385, s1=0.4357 s2=0.5485
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