At a nearby college, there is a school-sponsored website that matches people looking for roommates. According to the school's reports, 46% 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, 65 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 46%. (a) State the null hypothesis Ho and the alternative hypothesis H, that you would use for the test. Ho: 0 H₁: 0 Р np=0 n (1-p)=0 OO Ayis E

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. The value of the test statistic is given by
n
• The p-value is two times the area under the curve to the left of the value of the test statistic.
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.
р-р
p(1-p)
Step 4: Enter the p-value.
(Round to 3 decimal places.)
2
1
0.4
0.3
0.2+
2
A
pañol
?
Transcribed Image Text:. The value of the test statistic is given by n • The p-value is two times the area under the curve to the left of the value of the test statistic. 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. р-р p(1-p) Step 4: Enter the p-value. (Round to 3 decimal places.) 2 1 0.4 0.3 0.2+ 2 A pañol ?
At a nearby college, there is a school-sponsored website that matches people looking for roommates. According to the school's reports, 46% 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, 65 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 46%.
(a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test.
0
A
B
Ho: D
H₁: 0
np=0
n(1-p) =
Р
Explanation
<
Check
D
$
X
. The value of the test statistic is given by
X
(c) Perform a Z-test and find the p-value.
Here is some information to help you with your Z-test.
SO
(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.) Here n is the sample size and p is the population proportion you are testing.
Ś
=
<O
Ś
P P
p(1-p)
%
#
&
Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Terms of Use
*
0/5
C
с
Privacy Center | Accessibility
Ayishatu V
Aa
A
Español
?
delete
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, 46% 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, 65 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 46%. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. 0 A B Ho: D H₁: 0 np=0 n(1-p) = Р Explanation < Check D $ X . The value of the test statistic is given by X (c) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. SO (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.) Here n is the sample size and p is the population proportion you are testing. Ś = <O Ś P P p(1-p) % # & Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Terms of Use * 0/5 C с Privacy Center | Accessibility Ayishatu V Aa A Español ? delete
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