3. Mini-Mart, a nationwide convenience store, stated in the Wall Street Journal

Question

3. Mini-Mart, a nationwide convenience store, stated in the Wall Street Journal that they would not open a store in any location unless the mean store income in the neighborhood is at least $12,000. A random sample of 200 families in a given neighborhood produces a mean income of $11,852 with a sample standard deviation of $1,517 Establish the appropriate null and alternative hypotheses and test at the =0.02 level of significance whether Mini-Mart should open their store if all other criteria for a desirable location are met. a. b. What is the p-value of the test statistic and explain its significance?

Explanation / Answer

Below are the null and alternate hypothesis
H0: mu = 12000
H1: mu < 12000

sample mean = 11852

Test statistics, z = (11852 - 12000)/(1517/sqrt(200)) = -1.3797

p-value = 0.0838

As p-value is greater than the significance level of 0.2, we fail to reject the null hypothesis.

This means there are not sufficient evidence to conclude that average average income of the neighborhood is less than 12000.

Store can be opened

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