Please solve and show all work used to derive answer. Thank you. The manager of
ID: 3157470 • Letter: P
Question
Please solve and show all work used to derive answer. Thank you.
The manager of a supermarket would like the variance of waiting times of the customers not to exceed 3 min2. She would add another cash register if the variance exceeds this threshhold. She regularly checks the waiting times of the customers to ensure that the variance does not rise above the allowed level. In a recent random sample of 28 customer waiting times, she computes the sample variance as 4.2 min2. She believes that waiting times are normally distributed. Test to see if the variance exceed the threshold using significance level=.05.
Explanation / Answer
H0:sigma^2<=sigma0^2
H1: sigma^2>sigma0^2
The test statistic is as follows:
T=(N-1)(s/sigma0)^2, where N is sample size, the ratio (s/sigma0) compares the sampl estandard deviation to target one.
=(28-1)(2.05/1.73)^2, s=sqrt 4.2, sigma=sqrt 3
=37.91
Reject H0, if T>X^2N-1,1-alpha
The X^227,0.95=16.151
The test statistic is greate than 16.151, therefore, reject H0 to conlude that variance exceeds th ethreshold.