At a nearby college, there is a school-sponsored website that matches people looking for roommates. According to the school's reports, 44% of students will find a match their first time using the site. A writer for the school newspaper tests this claim by choosing a random sample of 165 students who visited the site looking for a roommate. Of the students surveyed, 57 said they found a match their first time using the site.Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.10 level of significance, to reject the claim that the proportion, \( p \), of all students who will find a match their first time using the site is 44%.a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \) that you would use for the test.- The diagram shows two boxes for input with symbols P, \( \hat{P} \), along with mathematical operators and a '?' indicating options to choose from for the hypothesis notation. \( H_0 \): □\( H_1 \): □b) For your hypothesis test, you will use a Z-test. Find the values of \( np \) and \( n(1-p) \) to confirm that a Z-test can be used. (One standard is that \( np \geq 10 \) and \( n(1-p) \geq 10 \) under the assumption that the null hypothesis is true.) Here \( n \) is the sample size and \( p \) is the population proportion you are testing. ### Transcription(d) Based on your answer to part (c), choose what can be concluded, at the 0.10 level of significance, about the claim made in the school’s reports.- O Since the value of the test statistic lies in the rejection region, the null hypothesis is rejected. So, there is enough evidence to reject the claim that 44% of students will find a match their first time using the site. - O Since the value of the test statistic lies in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to reject the claim that 44% of students will find a match their first time using the site. - O Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is rejected. So, there is enough evidence to reject the claim that 44% of students will find a match their first time using the site. - O Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to reject the claim that 44% of students will find a match their first time using the site.### Diagram ExplanationThe image includes a graph representing a probability distribution with a rejection region. The x-axis is labeled with values ranging from -3 to 3, indicating the standard score (z-scores) in a normal distribution. The curve represents the normal distribution, with areas shaded to signify the rejection regions on both tails. The exact values of critical z-scores are not visible, but they typically range above or below a certain threshold depending on the significance level (in this case, 0.10). The graph assists in visually determining if the computed test statistic falls within a region where the null hypothesis can be rejected or not.

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Answered: At a nearby college, there is a…

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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At a nearby college, there is a school-sponsored website that matches people looking for roommates. According to the school's reports, 42% of students will find a match their first time using the site. A writer for the school newspaper tests this claim by choosing a random sample of 170 students who visited the site looking for a roommate. Of the students surveyed, 86 said they found a match their first time using the site. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to reject the claim that the proportion, p, of all students who will find a match their first time using the site is 42%. (a) State the null hypothesis H, and the alternative hypothesis H, that you would use for the test. H₁: p=0.42 H₁: p = 0.42 020 0=0 ロッロロロ (b) For your hypothesis test, you will use a Z-test. Find the values of p and (1-p) to confirm that a Z-test can be used. (One standard is that np ≥ 10 and (1-p) ≥10 under the assumption…

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