### Hypothesis Testing for Mean GPAIn this exercise, we are testing the claim that the mean GPA of night students is smaller than 2.8 at the 0.025 significance level. Here's the process to follow:#### Step 1: Define HypothesesThe null and alternative hypotheses are defined as follows:- Null Hypothesis (H₀): $ \mu = 2.8 $- Alternative Hypothesis (H₁): $ \mu < 2.8 $These hypotheses are designed to test if the mean GPA ($ \mu $) of night students is less than 2.8.#### Step 2: Determine the Test TypeWe need to decide on the direction of the test. Since the alternative hypothesis states that the mean GPA is "less than" 2.8, this is a left-tailed test.- **Select the test type:** - Left-tailed (checked) - Right-tailed - Two-tailed#### Step 3: Sample DataIn this case, we have the following sample data based on 30 students:- Sample Mean GPA ($ \bar{x} $): 2.79- Standard Deviation (s): 0.03#### Step 4: Calculate Test StatisticWe will use the sample data to calculate the test statistic. The formula for the test statistic (t) is:\[ t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}} \]Where:- $ \bar{x} $ is the sample mean- $ \mu $ is the population mean under the null hypothesis- $ s $ is the sample standard deviation- $ n $ is the sample size#### Step 5: Find p-valueUsing the test statistic calculated, we can then find the p-value. - **The Test Statistic is:** (input box for two decimal places)- **The p-value is:** (input box for two decimal places)#### Step 6: Make a DecisionBased on the p-value and the significance level (0.025), we will make a decision:- If the p-value is less than 0.025, we **reject the null hypothesis**.- If the p-value is greater than or equal to 0.025, we **fail to reject the null hypothesis**.- **

The null and alternative hypothesis would be: Но: и — 2.8 Нo:p 2 0.7 Но:р < 0.7 Но:р — 0.7 Но:д 2 2.8 Но:Д < 2.8 Hi:р + 2.8 Ні:р< 0.7 Hі:p > 0.7 Hi:р +0.7 Hi:д < 2.8 Ні:д > 2.8 The test is:

The null and alternative hypothesis would be: Но: и — 2.8 Нo:p 2 0.7 Но:р < 0.7 Но:р — 0.7 Но:д 2 2.8 Но:Д < 2.8 Hi:р + 2.8 Ні:р< 0.7 Hі:p > 0.7 Hi:р +0.7 Hi:д < 2.8 Ні:д > 2.8 The test is:

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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