### Hypothesis Testing for Mean GPA of Night Students**Objective:** Test the claim that the mean GPA of night students is smaller than 2.1 at the 0.025 significance level.**Hypotheses:** - **Null and Alternative Hypotheses:** - \( H_0: \mu = 2.1 \) - \( H_1: \mu < 2.1 \)**Type of Test:** - **Left-tailed****Sample Data:**- **Sample Size:** 40- **Sample Mean GPA:** 2.08- **Standard Deviation:** 0.02**Calculations Required:**- **Test Statistic:** (To be calculated and reported to 2 decimal places)- **Critical Value:** (To be calculated and reported to 2 decimal places)**Decision Rule:**- Based on the calculations, we decide to: - Reject the null hypothesis - Fail to reject the null hypothesisMake sure to calculate the test statistic and critical value to complete the hypothesis test, determining whether the claim that the mean GPA is less than 2.1 is statistically supported.

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Description: ### Hypothesis Testing for Mean GPA of Night Students**Objective:** Test the claim that the mean GPA of night students is smaller than 2.1 at the 0.025 significance level.**Hypotheses:** - **Null and Alternative Hypotheses:** - \( H_0: \mu = 2.1

State the hypotheses. That is, there is no evidence to conclude that the mean GPA of night students is smaller than 2.1 That is, there is evidence to conclude that the mean GPA of night students is smaller than 2.1 Correct option: Option 6 Determine the tail of the test used here, Given the claim is the mean GPA of night students is smaller than 2.1. The word “ smaller” indicates that the tail of test is left tailed. Correct option: left tailed.Obtain the value of the test statistic. The value of the test statistic is obtained below: Thus, the value of the test statistic is –6.33.Obtain the degrees of degrees of freedom. The degrees of freedom are obtained below: From the information, given that there is a sample of 40. Thus, the degrees of freedom used are 39. Obtain the critical value. Use EXCEL Procedure for finding the critical value of t at the 0.025 significance level. Follow the instruction to obtain the critical value: Open EXCEL Go to Formula bar. In formula bar enter the function as“=TINV” Enter the probability value as 0.05. Enter the degrees of freedom as 39. Click enter EXCEL output: From the EXCEL output, the critical value of t at the 0.05 significance level for one tailed test with the 39 degrees of freedom is –2.02. Thus, the critical value is –2.02. The conclusion is obtained as shown below: Conclusion based on critical value approach: Use the level of significance is 0.05. The value of test statistic is –6.33 and the critical value is –2.02. By rejection rule, reject the null hypothesis. Correct option: Option 1 That is, there is evidence to conclude that the mean GPA of night students is smaller than 2.1

Math

Statistics

Test the claim that the mean GPA of night students is smaller than 2.1 at the .025 significance level. The null and alternative hypothesis would be: Ho:p = 0.525 Ho: µ = 2.1 Họ:p = 0.525 Ho:µ = 2.1 H9:p= 0.525 Họ:µ= 2.1 H1:p > 0.525 Hị:4 > 2.1 H1:p + 0.525 Hị:µ# 2.1 H:p< 0.525 H1:µ < 2.1 The test is: left-tailed two-tailed right-tailed Based on a sample of 40 people, the sample mean GPA was 2.08 with a standard deviation of 0.02 |(to 2 decimals) The test statistic is: The critical value is: (to 2 decimals) Based on this we: Reject the null hypothesis O Fail to reject the null hypothesis

Test the claim that the mean GPA of night students is smaller than 2.1 at the .025 significance level. The null and alternative hypothesis would be: Ho:p = 0.525 Ho: µ = 2.1 Họ:p = 0.525 Ho:µ = 2.1 H9:p= 0.525 Họ:µ= 2.1 H1:p > 0.525 Hị:4 > 2.1 H1:p + 0.525 Hị:µ# 2.1 H:p< 0.525 H1:µ < 2.1 The test is: left-tailed two-tailed right-tailed Based on a sample of 40 people, the sample mean GPA was 2.08 with a standard deviation of 0.02 |(to 2 decimals) The test statistic is: The critical value is: (to 2 decimals) Based on this we: Reject the null hypothesis O Fail to reject the null hypothesis

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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