Question

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-two fashion outlets who stock her skirts finds that the average price charged is $52.05 with the standard deviation being $4.68.

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 1% 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 1% level of significance? Type yes or no.
5. If in fact the retailers are charging $52.95 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 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.

Answer 1

(1)

Correct option:

gt

Explanation:
H0: Null Hypothesis: 49.95 ( Retailers are not undermining this image, and cutting her market share, by pricing them above her recommended retail price of $49.95 )

HA: Alternative Hypothesis: 49.95 ( Retailers are undermining this image, and cutting her market share, by pricing them above her recommended retail price of $49.95 ) (claim)

(2)

2.4528

Explanation:

= 0.01

ndf = n - 1 = 32 - 1 = 31

One side - Right Side Test

From Table, critical value of t = 2.4528

(3)

the test statistic :

2.54

Explanation:

SE = s/

= 4.68/

= 0.8273

Test statistic is given by:

t = (52.05 - 49.95)/0.8273

= 2.54

(4)

Correct option:

yes

Explanation:
Since calculated value of t = 2.54 is greater than critical value of t = 2.4528, the difference is significant. Reject null hypothesis.

(5)

Correct option:

cd

Explanation:

If in fact the retailers are charging $52.95 on average, we have rejected the null hypothesis: 49.95 and the decision is correct.

(6)

Correct option:

yes

Explanation;

if the null hypothesis was rejected, we could conclude that fashion outlets seem to be charging more than the recommended retail price since in that case > 49.95.