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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 that the null hypothesis is true.) Here is the sample size and is the population proportion you are testing. np=71.4 n(1-p)-98.6 (c) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. ■ The value of the test statistic is given by P-P p(1-p) The p-value is two times the area under the curve to the right of the value of the test statistic. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) Step 3: Shade the area represented by the p-value. Step 4: Enter the p-value. (Round to 3 decimal places.) 02- 01- x (d) Based on your answer to part (c), choose what can be concluded, at the 0.05 level of significance, about the claim made In the school's reports. O Since the p-value is less than (or equal to) the level a i, there is

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 that the null hypothesis is true.) Here is the sample size and is the population proportion you are testing. np=71.4 n(1-p)-98.6 (c) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. ■ The value of the test statistic is given by P-P p(1-p) The p-value is two times the area under the curve to the right of the value of the test statistic. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) Step 3: Shade the area represented by the p-value. Step 4: Enter the p-value. (Round to 3 decimal places.) 02- 01- x (d) Based on your answer to part (c), choose what can be concluded, at the 0.05 level of significance, about the claim made In the school's reports. O Since the p-value is less than (or equal to) the level a i, there is

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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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 that the null hypothesis is true.) Here is the sample size and is the population proportion you are testing. np=71.4 n(1-p)-98.6 (c) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. ■ The value of the test statistic is given by P-P p(1-p) The p-value is two times the area under the curve to the right of the value of the test statistic. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) Step 3: Shade the area represented by the p-value. Step 4: Enter the p-value. (Round to 3 decimal places.) 02- 01- x (d) Based on your answer to part (c), choose what can be concluded, at the 0.05 level of significance, about the claim made In the school's reports. O Since the p-value is less than (or equal to) the level a i, there is
Transcribed Image Text: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 that the null hypothesis is true.) Here is the sample size and is the population proportion you are testing. np=71.4 n(1-p)-98.6 (c) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. ■ The value of the test statistic is given by P-P p(1-p) The p-value is two times the area under the curve to the right of the value of the test statistic. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) Step 3: Shade the area represented by the p-value. Step 4: Enter the p-value. (Round to 3 decimal places.) 02- 01- x (d) Based on your answer to part (c), choose what can be concluded, at the 0.05 level of significance, about the claim made In the school's reports. O Since the p-value is less than (or equal to) the level a i, there is
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