According to the 2010 US Census, the average number of residentsper housing
unit for the n=87 counties in Minnesota was 2.10, and thestandard deviation
was 0.38. Test whether the true mean number of residents perhousing unit
in Minnesota in 2010 is less than the national value of 2.34 atthe level
?
= 0
.
05.
a. Show all five steps of this test.
b. What type of error could we be making in this context?
c. What is the minimum average number of residents per householdneeded
in order to fail to reject H0? Assume the sample standarddeviation is the same.
d. Suppose the true number of residents per household inMinnesota is normally
distributed with a mean of 2.0 and a standard deviation of 0.4.Suppose we reject
the null hypothesis if the sample means the number of residentsis less than 2.27. What
is the probability of making a type II error?
