A company is developing a new high performance wax for cross country ski racing.

Question

A company is developing a new high performance wax for cross country ski racing. In order to justify the price marketing wants, the wax needs to be very fast. Specifically, the mean time to finish their standard test course should be less than 55 seconds for a former Olympic champion. To test it, the champion will ski the course 8times. Complete parts a and bbelow. a) The champion's times (selected at random) are 58.1, 62.1, 47.7, 51.5, 48.7, 46.3, 50.5, and 43.6 seconds to complete the test course. Should they market the wax? Assume the assumptions and conditions for appropriate hypothesis testing are met for the sample. Assume s 0.05. Choose the correct null and alternative hypotheses below. A. Hou 55 O B. Ho 55 HA 55 HAH 55 O C. Hou 55 O D. Ho" 55 HAH 55 A 555

Explanation / Answer

(a) Ho: = 55 vs Ha: < 55

Data:    

n = 8   

= 55   

s = 6.177   

x-bar = 51.0625   

Hypotheses:    

Ho: ³ 55   

Ha: < 55   

Decision Rule:    

= 0.05   

Degrees of freedom = 8 - 1 = 7

Critical t- score = -1.894578604   

Reject Ho if t < -1.894578604   

Test Statistic:    

SE = s/Ön = 6.177/8 = 2.183899294

t = (x-bar - )/SE = (51.0625 - 55)/2.18389929369465 = -1.802967752

p- value = 0.057193246   

Decision (in terms of the hypotheses):    

Since -1.802967752 > -1.894578604 we fail to reject Ho

Conclusion (in terms of the problem):    

There is no sufficient evidence that < 55 (Option C)

(b) Option D.

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