A study is performed in a large southern town to determine w

A study is performed in a large southern town to determine whether the average weekly grocery bill per four-person family in the town is significantly different from the national average. The national average grocery bill is $100. A random sample of 30 families is taken in the town, and the mean is found to be 103.91 with a standard deviation of 8.57.

For each item below, please show your work and/or explain your reasoning to receive full credit.

a). Identify the null and alternative hypotheses for this situation.

b). Assuming a 0.05 level of significance, compute the appropriate test statistic.

c). Can you reject the null hypothesis? Explain/justify your response using numbers and words.

Solution

a)

Hypothesis:

Ho : u = 100

Ha: u != 100

b)

critical values Za= +/- 1.96

test static Z = 103.91 - 100/8.57/sqrt(30) = 2.499

c)

the critical region is Z > Za or Z < Za

since test static falls into critical region , we reject null hypothesis