Question

The new NikeGreen tennis shoe is made from renewable materials so that the shoe is both "green," and also costs less to manufacture than the typical tennis shoe. The industry average cost of manufacturing a typical tennis shoe is at least $2.47 per shoe. Nike believes it can use this lower production cost advantage and the "green" raw materials as a marketing tool in advertising the NikeGreen.

Nike wants to test if the NikeGreen actually does cost less to produce than the industry average as the cost of the renewable materials fluxuates. A sample of 9 prototype shoes are tested, and the average cost per shoe in the sample was $2.25 with a standard deviation per prototype in the sample of $0.28.

Is there sufficient evidence that the NikeGreen costs less to produce than the typical tennis shoe at an α = .005?

A. Provide the appropriate hypothesis test criteria:

HO: μ	≥ ≤ =
HA: μ	< > ≠

B. Using the data from the sample, answer the five fill-in-the-blank questions, and make the correct hypothesis test conclusion.

Reject Ho if the test statistic of		is	> <	the critical value of
Reject Ho if the p-value of		is	<	the value of α of

Based on these results, we should:

• Reject Ho

• Accept Ho

C. Explain why

Answer 1

a)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 2.47 or H0 : mu >= 2.47
Alternative Hypothesis, Ha: μ < 2.47

b)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (2.25 - 2.47)/(0.28/sqrt(9))
t = -2.357

Hence reject H0 if t < -3.355

P-value = 0.0231

Reject Ho if the test statistic of -2.357 is < the critical value of -3.355
  
Reject Ho if the p-value of 0.0231 is <   the value of α of 0.005

Accept Ho

c)

p value > 0.005

answered by: anonymous