Suppose that a researcher wants to check to see if the average household income in
Webster Groves,Missouri,has changed from the $60,000 it was three years ago.The
Researcher takes a random sample of households in Webster Groves and finds that the average income of these households is $58,000.If the standard error of the mean for this sample is $500,what is the approximate value produced by the Z-test?
A)+ 4.00
B)+ 3.65
C)+2.00
D)─ 4.00
E)─ 3.65

Question

Quizplus · Accepted Answer

To conduct a Z-test, we need to calculate the test statistic:
Z = (sample mean - hypothesized mean) / standard error
Z = (58,000 - 60,000) / 500
Z = -2 / 500
Z = -0.004
Since we are testing if the mean income has decreased, we are interested in the left tail of the normal distribution. Looking up the corresponding probability for Z = -0.004 in a standard normal table or in a calculator, we find that the p-value is approximately 0.4987.
Since the p-value is greater than the significance level (let's assume it is 0.05), we fail to reject the null hypothesis that the mean income is still $60,000. Therefore, we can conclude that there is not enough evidence to suggest that the mean income has changed. 
The closest choice to our calculated Z-value of -0.004 is option D (-4.00). This is because the other answer choices have much larger values, which would indicate a much greater level of significance than the given p-value of 0.4987.

Suppose That a Researcher Wants to Check to See If