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 8 times. The​ champion's times​ (selected at​ random) are 57.3​,63.1​, 46.1​, 50.4​,46.4​, 47.2​, 53.1​, and 42.3 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. Use 0.05 as the​ P-value cutoff level.

t= ___

p-value=___

Answer 1

We normally assume that that champion's times are distributed. high Let u= Population mean of new performance wax's timer. We Null hypothesis is Ho : u=55 Hi & ac55. versus Test statistic t = 7 - 55 Sl J5 ña exi +42.3 Clix 57.3 + 63-1+ -- 8 50.7375: ñ = 525 1 Xi-*) S29 8 I Cxi - 50.7375)2 too 17 52 = TT 46.5169 - s = 6.8203. ts ㅠ 50.7375-55 6.8203/18 IT t - - 1:7676 p-value p(toucn $ 17676)

tnt = t8-1= ty P-value = p (tz *-7676). Using MS-Excel, p(t73-1.7676) - T.DLST (-7876, 7,1) 0.06 & x= 0.05 p-value (0.06) > a (0.05) Hence we do not reject Ho. Lanclude that performance of Dew wax in some as otevoetx. we conclude than mean time to finish standard tess score is to 55 seconds. So it is not less than 55. equal So They should not market the wax.