Question

A politician claims the mean household income in Indiana is $60,000. A reporter believes it is less than $60,000. The reporter selects a random sample of 50 Indiana households. The mean income computed from the 50 people surveyed is $56,000. (Assume the standard deviation in Indiana household income is $15,000.)

We wish to do a hypothesis test to determine whether this provides evidence (at the .05 level) that the mean household income is less than $60,000. You should complete this problem following the example on HB Chap. 6 p. 9, as was discussed in Friday's class.

a) What is the z-score for the hypothesis test described above?

b) What is the P-value for this hypothesis test?

c) What is the correct conclusion for this hypothesis test?

d) In which of the following situations would it be INCORRECT to conclude the alternative hypothesis (H_A)?

e) In conducting any hypothesis test, if P is "small" (such as P < .05) we can:

Answer 1

Here, the population mean() = 60,000

To test,

H0 : The mean household income is equal to 60,000

H1 : The mean household income is less than 60000

= 56000 , = 15000 , n = 50 and alpha = 0.05

Therefore, z = ( - )/(   / n)

=( 56000 - 60000 ) / 2121.32

= -1.885

a) z score for this test = -1.885

b) Corresponding p value = 0.029

c) Therefore, since p value(0.029) < alpha(0.05) , we reject the null hypothesis. We conclude that the population mean income is less than 60,000.

e) In conducting a hypothesis test, is p is small(<0.05) we can reject the null hypothesis at level 0.05.