A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. In testing the university’s belief, the appropriate hypotheses are __________. The image displays a list of four hypothesis test cases, each with a null hypothesis (\(H_0\)) and an alternative hypothesis (\(H_A\)). Here are the different hypotheses listed:1. **First Hypothesis Set:** - Null Hypothesis (\(H_0\)): \(p \leq 0.20\) - Alternative Hypothesis (\(H_A\)): \(p > 0.20\)2. **Second Hypothesis Set:** - Null Hypothesis (\(H_0\)): \(p \geq 0.20\) - Alternative Hypothesis (\(H_A\)): \(p < 0.20\)3. **Third Hypothesis Set:** - Null Hypothesis (\(H_0\)): \(\overline{p} = 0.15\) - Alternative Hypothesis (\(H_A\)): \(\overline{p} < 0.15\)4. **Fourth Hypothesis Set:** - Null Hypothesis (\(H_0\)): \(p = 0.15\) - Alternative Hypothesis (\(H_A\)): \(p \neq 0.15\)

Given that, The sample size is, n = 200 The number of students have a GPA of 3.00 or below is, x = 30 The population proportion is, p = 0.20 Claim: Test the proportion of graduates with a GPA of 3.00 or below is less than 0.20 The symbolic form of given claim is, p<0.20 The options (1), (3) and (4) are incorrect Reason for option (1): The hypothesis in option (1) is wrong because the notation of null and alternative hypothesis is taken as wrong and also the claim of the hypothesis is wrongly represented in the alternative hypothesis. Reason for option (3): The hypothesis in option (3) is wrong because the notation of null and alternative hypothesis is taken as wrong and also instead of population proportion and its value , the sample proportion and its value is taken in the hypothesis. Reason for option (4): The hypothesis in option (4) is wrong because the notation of null and alternative hypothesis is taken as wrong. The type of test is left tailed test but not two tailed test. The correct answer is option (2): The null hypothesis is, H0:The proportion of graduates with a GPA of 3.00 or below is greater than or equal to 0.20 That is, H0:p≥0.20 The alternative hypothesis is, H1:The proportion of graduates with a GPA of 3.00 or below is less than 0.20 That is, H1:p<0.20

Math

Statistics

A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. In testing the university’s belief, the appropriate hypotheses are __________.

A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. In testing the university’s belief, the appropriate hypotheses 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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