Test the hypothesis in Problem 10.1, by using the standard normal variable z as the test statistic.
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 involved household income can be assumed to be approximately normally distributed, and that the standard deviation can be accepted as being equal to σ = $2,000, based on an earlier study. For a random sample of n = 15 households, the mean household income is found to be X = $44,000. Test the null hypothesis that μ = $45,000 by establishing critical limits of the sample mean in terms of dollars, using the 5 percent level of significance.