2. You want to rent an unfurnished one-bedroom apartment for next semester. You

Question

2. You want to rent an unfurnished one-bedroom apartment for next semester. You take a random sample of 10 apartments advertised in the local newspaper and record the monthly rent. Here are the sample data: 500, 650, 600, 505, 450, 550, 515, 495, 650, 395 a. Find the sample mean b. Find the sample median c. Find the standard deviation d. Find the variance e. Find the range f. Construct a 95% confidence interval estimate of the population mean. (You may assume that the original population is normally distributed.) g. Use a 0.05 significance level to test the claim that the mean rent of all advertised apartments is greater than $500 per month.

Explanation / Answer

Given that,
population mean(u)=500
sample mean, x =531
standard deviation, s =82.79
number (n)=10
null, Ho: =500
alternate, H1: >500
level of significance, = 0.01
from standard normal table,right tailed t /2 =2.821
since our test is right-tailed
reject Ho, if to > 2.821
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =531-500/(82.79/sqrt(10))
to =1.1841
| to | =1.1841
critical value
the value of |t | with n-1 = 9 d.f is 2.821
we got |to| =1.1841 & | t | =2.821
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :right tail - Ha : ( p > 1.1841 ) = 0.13335
hence value of p0.01 < 0.13335,here we do not reject Ho
ANSWERS
---------------
null, Ho: =500
alternate, H1: >500
test statistic: 1.1841
critical value: 2.821
decision: do not reject Ho
p-value: 0.13335
no evidence that it is greater than 500

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