Hi~ can anyone help me with this question? Thanks a lot!!! Claudia Maurva, manuf

Question

Hi~ can anyone help me with this question? Thanks a lot!!!

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-six fashion outlets who stock her skirts finds that the average price charged is $52.19 with the standard deviation being $7.53.

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, reporting your answer to two decimal places.____________
4. Is the null hypothesis rejected for this test? Type yes or no. ___________
5. If in fact the retailers are charging the recommended retail price on average, determine the nature of the decision made in the test. Type cr (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 the null hypothesis was rejected, could we conclude that fashion outlets seem to be charging more than the recommended retail price? Type yes or no._________

Explanation / Answer

Recommended retail price = $49.95

Sample size n = 36; average price charged =$52.19 stdev s = $7.53

Null Hyp: The price charged is $49.95

H0: mu = 49.95

Alt Hyp: The price charged is greater than $49.95

Ha: mu > 49.95

Ans 1) gt

2) Degrees of Freedom = n - 1 = 35

   Sig level = 0.05

   Critical value = +1.689

3) Test stat t = (xbar - mu)/(stdev/sqrt(n)) = (52.19 - 49.95)/(7.53/sqrt(36)) = 1.79

4) Rejection region is test stat > critical value (1.689)

Since test stat lies in the rejection region we reject the Null hypothesis

Ans) Yes

5) a. Type 1 error was made

Reason: We incorrectly reject a True Null hypothesis

6) Yes (Since there is evidence to support the claim as null is rejected)

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