Project Part B
In regards to the dataset from AJ Department store, your manager has speculated the following: the average (mean) annual income is less than $50,000, the true population proportion of customers who live in an urban area exceeds 40%, the average (mean) number of years lived in the current home is less than 13 years, the average (mean) credit balance for suburban customers is more than $4300.
Part 1. Using the sample data, perform the hypothesis test for each of the above situations in order to see if there is evidence to support your manager’s belief in each case a.-d. In each case use the Seven Elements of a Test of Hypothesis, in Section 6.2 of your text book with α = .05, and explain your conclusion in simple terms. Also be sure to compute the p-value and interpret.
Our textbook tells us the following are the elements used to test a hypothesis:
Elements of a Test of Hypothesis
1. Null hypothesis (H0): A theory about the specific values of one or more population parameters. The theory generally represents the status quo, which we adopt until it is proven false. The theory is always stated as H0: parameter = value.
2. Alternative (research) hypothesis (Ha): A theory that contradicts the null hypothesis. The theory generally represents that which we will adopt only when sufficient evidence exists to establish its truth.
3. Test statistic: A sample statistic used to decide whether to reject the null hypothesis.
4. Rejection region: The numerical values of the test statistic for which the null hypothesis will be rejected. The rejection region is chosen so that the probability is α that it will contain the test statistic when the null hypothesis is true, thereby leading to a Type I error. The value of α is usually chosen to be small (e.g., .01, .05, or .10) and is referred to as the level of significance of the test.
5. Assumptions: Clear statement(s) of any assumptions made about the