Question

1. Which of the following is the value of X2α/2,dfXα/2,df2 for a 99% confidence level and degrees of freedom equal 6.

16.812

18.548

0.872

0.676

2.

We conduct the following hypothesis test H0:σ2=82,HA:σ2≠82H0:σ2=82,HA:σ2≠82. For a random sample of 15 observations, the sample standard deviation is 12. Which of the following is the correct approximation of the p-value used to conduct this test?

p-value lies between 0.025 and 0.05

p-value lies between 0.01 and 0.025

p-value lies between 0.05 and 0.10

p-value is greater than 0.10

3.

The manager of a video library would like the variance of the waiting times of the customers not to exceed 2.30 minutes-squared. He would like to add an additional billing counter if the variance exceeds the cut-off. He checks the recent sample data. For a random sample of 24 customer waiting times, he arrives at a sample variance of 3.8 minutes-squared. The manager assumes the waiting times to be normally distributed. Which of the following is the correct approximation of the p-value used to conduct this test?

p-value lies between 0.005 and 0.010

p-value lies between 0.010 and 0.025

p-value lies between 0.050 and 0.10

p-value lies between 0.025 and 0.05

Answer 1

1)
chi^2(alpha/2,df ) = 0.676

2)

This is a two tailed test

chi^2 = (n-1)s^2/sigma^2
= ((15-1) * 12^2)/82
= 24.585

p value =0.0778

p-value lies between 0.05 and 0.10

3)

This is a one tailed test

chi^2 = (n-1)s^2/sigma^2
= ((24 - 1) * 3.8)/2.30
= 24.585

p value =0.001

p-value lies between 0.005 and 0.010