Question

A representative of a community group informs the prospective developer of a shopping center that the average income per household in the area is $45 000. Suppose that for the type of area the observed household income can be assumed to be approximately normally distributed, and that the standard deviation can be accepted as being equal to $2000, based on an earlier study. In a random sample of 15 households, the mean household income is found to be $44 000. test the null hypothesis m $45000, by establishing critical limits of the sample mean in terms of dollars, using the 5 percent level of significance

Answer 1

H0: Null Hypothesis: = 45000 ( the average income per household in the area is $45 000 ) (Claim)

HA: Alternative Hypothesis: 45000 ( the average income per household in the area is not $45 000 )

= 44000

n = 15

= 2000

= 0.05

From Table, critical values of Z = 1.96

Test Statistic is given by:

Since calculated value of Z = - 1.936 is greater than critical value of Z = - 1.96, the difference is not significant. fail to reject null hypothesis.

Conclusion:
The data support the claim that the average income per household in the area is $45 000.