### Research Question:A researcher is interested in understanding if there is a difference in the proportion of undergrad and grad students at UCI who prefer online teaching to in-person teaching, at the α = 0.05 level. They take 2 samples, first, a sample of 300 undergrad students. The second, is a sample of 172 grad students. Of the undergrads, 186 said they preferred online lectures, and of the graduate students, 104 said that they prefer online lectures. Let \( p_1 \) be the proportion of undergrad students who prefer online classes and \( p_2 \) be the proportion of grad students who prefer online lectures.#### (a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret them in context of the problem).**Solution:**- Null Hypothesis (\(H_0\)): \( p_1 = p_2 \) - There is no difference in the proportion of undergrad and grad students who prefer online teaching.- Alternative Hypothesis (\(H_A\)): \( p_1 \neq p_2 \) - There is a difference in the proportion of undergrad and grad students who prefer online teaching.#### (b) Calculate the test statistic.**Solution:**To calculate the test statistic, use the following steps:1. Calculate the sample proportions: - \(\hat{p}_1 = \frac{186}{300}\) - \(\hat{p}_2 = \frac{104}{172}\)2. Calculate the pooled proportion (\(\hat{p}\)): - \(\hat{p} = \frac{186 + 104}{300 + 172}\)3. Calculate the standard error (SE): - \( SE = \sqrt{\hat{p}(1 - \hat{p}) \left(\frac{1}{n_1} + \frac{1}{n_2}\right)} \)4. Calculate the test statistic (\(z\)): - \( z = \frac{\hat{p}_1 - \hat{p}_2}{SE} \)#### (c) Calculate the critical value.**Solution:**For a two-tailed test at the α = 0.05 level, the critical values for \(z\) are approximately ±1.96.#### (d) Draw a picture of the distribution of the

Since we only do up to three sub parts of a problem, we'll be doing the first three sub parts only.…

Answered: A researcher is interested in…

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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