Suppose that a new trail running shoe was test marketed in the Des Moines, IA and Toledo, OH metropolitan areas. Equal amounts of money were spent on advertising in the two areas. However, different advertising media were employed in the two areas. Advertising in Des Moines was done entirely on television, while advertising in Toledo consisted of mixture of television, radio, newspaper and magazine ads. Two months after the advertising campaigns commenced, surveys are taken to estimate consumer awareness of the product. In Des Moines, 631 out of 1000 randomly chosen consumers are aware of the new shoe. In Toledo, 798 out of the 1000 randomly selected consumers are aware of the new shoe. It is desired to check if using more media resources resulted in increased awareness about the new shoe in Toledo, OH.
(a) Set up the relevant null and alternative hypothesis. (b) Write down the test statistic to be used for testing the hypothesis.
(c) Are the assumptions satisfied to test the hypothesis? (d) What is the sampling distribution of the test statistic if the null hypothesis is true?
(e) If the level of significance α = 5%, write down the rejection region. (f) Based on the data, do you reject the null hypothesis? Justify.
(g) Did you commit a type I error based on your conclusion to 2f above?