Question

Bjork Larsen was trying to decide whether to use a new racing wax for cross-country skis. He decided that the wax would be worth the price if he could average less than 55 seconds on a course he knew well, so he planned to study the wax by racing on the course 8 times. His 8 race times were 56.3, 65.9, 50.5, 52.4, 46.5,57.8, 52.2, and 43.2 seconds. Should he buy the wax? Explain by preforming an appropriate hypothesis test.

Answer 1

n = 8

sample mean =

standard deviation = S = 7.03

claim : The wax would be worth the price if he could average less than 55 seconds on a course.

Null and alternative hypothesis is

Level of significance = 0.05

Here population standard deviation is not known so we use t-test statistic.

Test statistic is

Degrees of freedom = n - 1 = 8-1=7

P-value = 0.2348 ( using t table)

P-value , Failed to Reject H0

conclusion : There is insufficient evidence to support the claim that the wax would be worth the price if he could average less than 55 seconds on a course.