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 160 students who visited the site looking for a roommate. Of the students surveyed, 77 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 44%. (a) State the null hypothesis H, and the alternative hypothesis H, that you would use for the test. H,: 0 ロ<ロ OSO H,: 0 ロォロ (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 2 10 and n(1-p) > 10 under the assumption that the null hypothesis is true.) Here n is the sample size andp is the population proportion you are testing.

MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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Answer the following questions on first and second picture and show your solution.

(c) Perform a Z-test and find the p-value.
Here is some information to help you with your Z-test.
PP
• The value of the test statistic is given by
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
O Two-tailed
03+
Step 2: Enter the test statistic.
(Round to 3 decimal places.)
02
Step 3: Shade the area represented by
the p-value.
0.1-
Step 4: Enter the p-value,
(Round to 3 decimal places.)
2.
(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 of significance, 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 p-value is less than (or equal to) the level of significance, 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 p-value is greater than the level of significance, 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 p-value is greater than the level of significance, 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.
Transcribed Image Text:(c) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. PP • The value of the test statistic is given by 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 O Two-tailed 03+ Step 2: Enter the test statistic. (Round to 3 decimal places.) 02 Step 3: Shade the area represented by the p-value. 0.1- Step 4: Enter the p-value, (Round to 3 decimal places.) 2. (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 of significance, 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 p-value is less than (or equal to) the level of significance, 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 p-value is greater than the level of significance, 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 p-value is greater than the level of significance, 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.
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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, 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 160 students who visited the site
looking for a roommate. Of the students surveyed, 77 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 44%.
(a) State the null hypothesis H, and the alternative hypothesis H, that you would use for the test.
H: 0
OSO
H,: 0
D=0
ロロ
(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 2 10
and n(1-p) 2> 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.
np=0
n(1-p) =0
Transcribed Image Text:1 3. 6 8 9. 10 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 160 students who visited the site looking for a roommate. Of the students surveyed, 77 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 44%. (a) State the null hypothesis H, and the alternative hypothesis H, that you would use for the test. H: 0 OSO H,: 0 D=0 ロロ (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 2 10 and n(1-p) 2> 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. np=0 n(1-p) =0
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