Question: You earned another new customer account with Wainwright Lawn and Garden Company. Marketing manager Bill Williams believes that the average income for the company’s customers is less than $30,000.00. Williams made this claim to defend his selection of brands aimed at lower-income customers. To verify the claim, he took a simple random sample of 400 customers and conducted a survey to determine their income levels. The assumption is that ? = $4,000. The significance level is 0.10. If the actual mean income is $29,800, determine the probability that the test will mistakenly lead the managers to “accept” the null hypothesis.

a) Specify the null and alternative hypotheses, and determine the critical value z_a.

b) Calculate the critical value x_a.

c) Compute the test statistic.

d) Determine Beta.