At a neighboring university there is a website sponsored by the institution that matches people looking for roommates. According to university reports, the35% of students will find a partner the first time they use the website. A writer for the college newspaper tests this claim by choosing a random sample of 170 students who used the website to search for a roommate. Of the students surveyed,64they said they found a partner the first time they used the website. Complete the parts below to perform a hypothesis test to see if there is sufficient evidence, at the significance level of0.05, to reject the claim that the proportion,p, of all students who are going to find a partner the first time they use the website is35%. (to) Formulate the null hypothesish and the alternative hypothesish that you will use in your test. 믐 0<0 OSO O>0 20 X 0=0 tools help (b) In this hypothesis test, you will use a testZ. Find the values of pandn61-p)to confirm that a Z test can be used. (A standard is that p≥10and n61-p)>10under the assumption that the pull hypothesis is true). In this case the sample size and is the proportion of the population that you

At a neighboring university there is a website sponsored by the institution that matches people looking for roommates. According to university reports, the35% of students will find a partner the first time they use the website. A writer for the college newspaper tests this claim by choosing a random sample of 170 students who used the website to search for a roommate. Of the students surveyed,64they said they found a partner the first time they used the website. Complete the parts below to perform a hypothesis test to see if there is sufficient evidence, at the significance level of0.05, to reject the claim that the proportion,p, of all students who are going to find a partner the first time they use the website is35%. (to) Formulate the null hypothesish and the alternative hypothesish that you will use in your test. 믐 0<0 OSO O>0 20 X 0=0 tools help (b) In this hypothesis test, you will use a testZ. Find the values of pandn61-p)to confirm that a Z test can be used. (A standard is that p≥10and n61-p)>10under the assumption that the pull hypothesis is true). In this case the sample size and is the proportion of the population that you

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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Question

At a neighboring university there is a website sponsored by the institution that matches people looking for roommates. According to university reports, the35%
of students will find a partner the first time they use the website. A writer for the college newspaper tests this claim by choosing a random sample of 170
students who used the website to search for a roommate. Of the students surveyed, 64they said they found a partner the first time they used the website.
Complete the parts below to perform a hypothesis test to see if there is sufficient evidence, at the significance level of0.05, to reject the claim that the
proportion,p,of all students who are going to find a partner the first time they use the website is35%.
(to) Formulate the null hypothesish and the alternative hypothesish that you will use in your test.
ho:0
h₁:0
Р
np=
O<0 OSO
ロミロ
X
P
X
O>0
ロ=ロ ☐#0
(b) In this hypothesis test, you will use a testZ. Find the values ofnpandn 61-p)to confirm that a Z test can be used . (A standard is thatnp≥10and
n61-p) ≥10under the assumption that the null hypothesis is true). In this case, is the sample size and is the proportion of the population that you
are testing.
tools help
Ś

nol-p)= ||
(c) Carry out a testZ. _ This information can be used to carry out your testZ. _
●
• Z0.025 is the value that delimits an area of0.025in the right tail of the distribution.
The value of the test statistic is given byz =
standard normal distribution
Step 1: Select one queue or two
queues.
A tail
two tails
Step 2: Enter the critical value(s).
(Round to 3 decimal places.
Step 3: Enter the test statistic.
(Round to 3 decimal places.
р-р
p(1-p)
no
04
0.3 +
0.2 +
0.1 +

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Step 2: State the null and alternative hypotheses:

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Step 3: Find the value of np and n(1-p):

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Step 4: c. Conduct a test to check the significance:

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Follow-up Questions

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Follow-up Question

(d) Based on your answer to part (c), choose what can be concluded, at the significance level of0.05, about the claim in the
university report.
Since the value of the test statistic is in the rejection region, the null hypothesis is rejected. Therefore, there is
sufficient evidence to reject the claim that the35%of students will find a partner the first time they use the
website.
Since the value of the test statistic is in the rejection region, the null hypothesis is not rejected. Therefore,
there is insufficient evidence to reject the claim that the35%of students will find a partner the first time they
use the website.
Since the value of the test statistic is not in the rejection region, the null hypothesis is rejected. Therefore,
there is sufficient evidence to reject the claim that the35%of students will find a partner the first time they use
the website.
Since the value of the test statistic is not in the rejection region, the null hypothesis is not rejected. Therefore,
there is insufficient evidence to reject the claim that the35%of students will find a partner the first time they
use the website.
X
Ś

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