Statement of a problem № m1408


An article in a trade journal reports that nationwide 28% of liquor purchases are made by women. If B & B Liquor’s proportion of sales to women is significantly different from the national norm, the owners are considering redesigning B & B’s advertising. A random sample of 100 customers is selected resulting in 24 women and 76 men. Does the sample data provide evidence to conclude that less than 28% of B&B’s customers are women (using a = .01)? Use the hypothesis testing procedure outlined below. a. Formulate the null and alternative hypotheses. b. State the level of significance. c. Find the critical value (or values), and clearly show the rejection and non-rejection regions. d. Compute the test statistic. e. Decide whether you can reject Ho and accept Ha or not. f. Explain and interpret your conclusion in part e. What does this mean? g. Find the observed p-value for the hypothesis test and interpret this value. What does this mean? h. Does this sample data provide evidence (with a = .01), that less than 28% of B & B’s customers are women?

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