Claudia Maurva, manufacturer of CM denim skirts, has pitched her advertising to develop a "stylish yet affordable" image for her brand. She is concerned, however, that retailers are undermining this image, and cutting her market share, by pricing them above her recommended retail price of $49.95. A random sample of thirty-five fashion outlets who stock her skirts finds that the average price charged is $51.87 with the standard deviation being $6.96.
1. State the direction of the alternative hypothesis used to test the company's claim. Type the letters gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box.
2. Use the tables in the text to determine the critical value used to conduct the test, assuming a 5% level of significance. If there are two critical values, state only the positive value.
3. Calculate the test statistic (two decimal places).
4. Is the null hypothesis rejected at the 5% level of significance? Type yes or no.
5. If in fact the retailers are charging $51.95 on average, determine the nature of the decision made in the test. Type cd (correct decision), 1 (a Type I error was made) or 2 (a Type II error was made) as appropriate.
6. Regardless of your answer for 4, if we failed to reject the null hypothesis, could we conclude that fashion outlets seem to be charging more than the recommended retail price? Type yes or no.