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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, 39% 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 160 students who visited the site looking for a roommate. Of the students surveyed, 54 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 39%. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. Ho: ê 믐 H₁: 0 np=0 n (1-P)- ● 5 (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 np210 and n (1-p)2 10 under the assumption that the null hypothesis is true.) Heren is the sample size and p is the population proportion you are testing. 5 Standard Normal p (c) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. Distribution O

At a nearby college, there is a school-sponsored website that matches people looking for roommates. According to the school's reports, 39% 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 160 students who visited the site looking for a roommate. Of the students surveyed, 54 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 39%. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. Ho: ê 믐 H₁: 0 np=0 n (1-P)- ● 5 (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 np210 and n (1-p)2 10 under the assumption that the null hypothesis is true.) Heren is the sample size and p is the population proportion you are testing. 5 Standard Normal p (c) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. Distribution O

MATLAB: An Introduction with Applications
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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80 At a nearby college, there is a school-sponsored website that matches people looking for roommates. According to the school's reports, 39% 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 160 students who visited the site looking for a roommate. Of the students surveyed, 54 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 39%. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. Ho: O 4 H₁: 0 $ np=0 n (1-p)= Standard Normal (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≥ 10 and n (1-p)≥10 under the assumption that the null hypothesis is true.) Heren is the sample size and p is the population proportion you are testing. 5 Distribution Step 1: Select one- tailed or two-tailed. O One-tailed O Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) (c) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. Step 3: Shade the area represented by the p-value. Continue P P □口 P=P p(1-P) n The p-value is two times the area under the curve to the left of the value of the test statistic. The value of the test statistic is given by D DOO 000 F4 X % 5 X OSO O=O F5 S -3 00 -2 (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. Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to reject the claim that 39% of students will find a 0.3 < 6 0.2- O.F F6 MacBook Air & 7 3 Submit Assignment 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility A S F7 X 8 Español F8 ( 9 F9 0 FIG
Transcribed Image Text:80 At a nearby college, there is a school-sponsored website that matches people looking for roommates. According to the school's reports, 39% 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 160 students who visited the site looking for a roommate. Of the students surveyed, 54 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 39%. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. Ho: O 4 H₁: 0 $ np=0 n (1-p)= Standard Normal (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≥ 10 and n (1-p)≥10 under the assumption that the null hypothesis is true.) Heren is the sample size and p is the population proportion you are testing. 5 Distribution Step 1: Select one- tailed or two-tailed. O One-tailed O Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) (c) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. Step 3: Shade the area represented by the p-value. Continue P P □口 P=P p(1-P) n The p-value is two times the area under the curve to the left of the value of the test statistic. The value of the test statistic is given by D DOO 000 F4 X % 5 X OSO O=O F5 S -3 00 -2 (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. Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to reject the claim that 39% of students will find a 0.3 < 6 0.2- O.F F6 MacBook Air & 7 3 Submit Assignment 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility A S F7 X 8 Español F8 ( 9 F9 0 FIG
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