ECON 106 - Homework 8

ECON106 HW8
1 Textbook questions, #s: 19.28, 19.32, 19.40
2 A random sample is obtained from a population with a variance of 625 and the sample mean is computed.Test the null hypothesis H0 :  < 100 versus the alternative HA :   100 for the given sample sizes. Compute the critical value xcrit at the = :05 level and state the decision rule (meaning when would you decide to reject).
a) n=25
b) n=44
3
A random sample of n=25 with variance = 
2 (this will change in the parts of the question below) and the sample mean is 70. Consider the null hypothesis H0 :  > 80 versus the alternative hypothesis
HA :   80. Compute the p-value for each part below and state if you would reject the null at the = 5% level:
a) 
2 = 225
b) 
2 = 900
c) 
2 = 400
3.1 Using the data from #3a) - c) above, calculate the p-value if the null hypothesis was H0 :  = 80 versus the alternative hypothesis HA :  6= 80.
a)
b)
c)
3.2 You conduct a hypothesis test using the data from #3a) above (the one-sided test). If the true population mean is 73, what is the power of a test conducted at the:
a) = :10 level
b) = :05 level
c) = :01 level