### Hypothesis Testing: Comparing Mean GPAs**Problem Statement:**You are testing the claim that the mean GPA of night students is less than the mean GPA of day students.**Sample Data:**- **Night Students:** - Sample Size (n₁): 35 - Sample Mean (x̄₁): 2.01 - Standard Deviation (s₁): 0.88- **Day Students:** - Sample Size (n₂): 45 - Sample Mean (x̄₂): 2.2 - Standard Deviation (s₂): 0.31**Objective:**Calculate the test statistic, rounded to 2 decimal places.Use the given sample data to determine if there is a statistically significant difference between the mean GPA of night students and day students by calculating the test statistic.**Test Statistic Calculation:**The test statistic for comparing two sample means can be calculated using the formula:\[ t = \frac{(\bar{X}_1 - \bar{X}_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \]Where:- \(\bar{X}_1\) and \(\bar{X}_2\) are the sample means of night and day students respectively.- \(s_1\) and \(s_2\) are the standard deviations of the night and day student samples respectively.- \(n_1\) and \(n_2\) are the sample sizes of night and day students respectively.1. Calculate the numerator (\(\bar{X}_1 - \bar{X}_2\)): \[ \bar{X}_1 - \bar{X}_2 = 2.01 - 2.2 = -0.19 \]2. Calculate the denominator (\(\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}\)): \[ s_1^2 = 0.88^2 = 0.7744 \] \[ s_2^2 = 0.31^2 = 0.0961 \] \[ \frac{s_1^2}{n_1} = \frac{0.7744}{35} \

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Description: ### Hypothesis Testing: Comparing Mean GPAs**Problem Statement:**You are testing the claim that the mean GPA of night students is less than the mean GPA of day students.**Sample Data:**- **Night Students:** - Sample Size (n₁): 35 - Sample Mean (x̄

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You are testing the claim that the mean GPA of night students is less than the mean GPA of day students. You sample 35 night students, and the sample mean GPA is 2.01 with a standard deviation of 0.88 You sample 45 day students, and the sample mean GPA is 2.2 with a standard deviation of 0.31 Calculate the test statistic, rounded to 2 decimal places

You are testing the claim that the mean GPA of night students is less than the mean GPA of day students. You sample 35 night students, and the sample mean GPA is 2.01 with a standard deviation of 0.88 You sample 45 day students, and the sample mean GPA is 2.2 with a standard deviation of 0.31 Calculate the test statistic, rounded to 2 decimal places

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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