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 170 students who visited the site looking for a roommate. Of the students surveyed, 60 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 Ho and the alternative hypothesis H₁ that you would use for the test. Ho: O Â H₁:0 p np=0 n(1-p) = 0<0 OSO 020 ローロ ロメロ X $ (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 22 (1-p) 10 under the assumption that the null hypothesis is true.) Here is the sample size and p is the population proportion you are testing. S O>0 (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(1-p) n The p-value is two times the area under the curve to the left of the value of the test statistic. Español 7 ∞ B

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6th Edition
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Author:Amos Gilat
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(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 i true.) Here 72 is the sample size and p is the population proportion you are testing.
np=0
n(1-p) = 0
(c) Perform a Z-test and find the p-value.
Here is some information to help you with your Z-test.
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
Standard Normal 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.)
Step 3: Shade the area represented by
the p-value.
5
Step 4: Enter the p-value.
(Round to 3 decimal places.)
0.3+
02-
0.1-
Espanol
81 @EÙ
Transcribed Image Text:(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 i true.) Here 72 is the sample size and p is the population proportion you are testing. np=0 n(1-p) = 0 (c) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. 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 Standard Normal 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.) Step 3: Shade the area represented by the p-value. 5 Step 4: Enter the p-value. (Round to 3 decimal places.) 0.3+ 02- 0.1- Espanol 81 @EÙ
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 170 students who visited the site
looking for a roommate. Of the students surveyed, 60 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 Ho and the alternative hypothesis H₁ that you would use for the test.
Ho: O
Â
H₁: 0
Р
np = 0
n (1-p) = 0
O<O
020 ローロ
OSO
X
Ś
(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 22 (1-p) ≥ 10 under the assumption that the null hypothesis is true.) Here is the sample size and p is the population proportion you are testing.
(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
O<O
0*0
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.
Español
?
00
B
!
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, 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 170 students who visited the site looking for a roommate. Of the students surveyed, 60 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 Ho and the alternative hypothesis H₁ that you would use for the test. Ho: O Â H₁: 0 Р np = 0 n (1-p) = 0 O<O 020 ローロ OSO X Ś (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 22 (1-p) ≥ 10 under the assumption that the null hypothesis is true.) Here is the sample size and p is the population proportion you are testing. (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 O<O 0*0 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. Español ? 00 B !
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