A travel agency claims that the variance of room rates of hotels in a certain ci

Question

A travel agency claims that the variance of room rates of hotels in a certain city is no more than $440. You work for a consumer advocacy group and are asked to test this claim. You find that the random sample of 29 hotels has a variance of $484. At (sigma) = 0.1 Do you have enough evidence to reject the claim? A travel agency claims that the variance of room rates of hotels in a certain city is no more than $440. You work for a consumer advocacy group and are asked to test this claim. You find that the random sample of 29 hotels has a variance of $484. At (sigma) = 0.1 Do you have enough evidence to reject the claim?

Explanation / Answer

Given that,
population variance (^2) =440
sample size (n) = 29
sample variance (s^2)=484
null, Ho: ^2 <440
alternate, H1 : ^2 >440
level of significance, = 0.1
from standard normal table,right tailed ^2 /2 =37.916
since our test is right-tailed
we use test statistic chisquare ^2 =(n-1)*s^2/o^2
^2 cal=(29 - 1 ) * 484 / 440 = 28*484/440 = 30.8
| ^2 cal | =30.8
critical value
the value of |^2 | at los 0.1 with d.f (n-1)=28 is 37.916
we got | ^2| =30.8 & | ^2 | =37.916
make decision
hence value of | ^2 cal | < | ^2 | and here we do not reject Ho
^2 p_value =0.326
ANSWERS
---------------
null, Ho: ^2 <=440
alternate, H1 : ^2 >440
test statistic: 30.8
critical value: 37.916
p-value:0.326
decision: do not reject Ho
no evidence to reject the claim

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