Bjork Larsen was trying to decide whether to use a new racing wax for cross coun
ID: 3391311 • Letter: B
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 test the wax by racing on the course 9 times. His 8 race times were 58.2, 56.3, 65.9, 50.5, 52.4, 46.5, 57.8, 52.2, and 43.2 seconds. Should he buy the wax? Justify your answer using appropriate t or z -test. Show process of hypothesis testing and test using 0.01 level of significance.Explanation / Answer
A)
Formulating the null and alternative hypotheses,
Ho: u >= 55
Ha: u < 55
**********************
B)
As we can see, this is a left tailed test.
Getting the test statistic, as
X = sample mean = 53.66666667
uo = hypothesized mean = 55
n = sample size = 9
s = standard deviation = 6.790802604
Thus, t = (X - uo) * sqrt(n) / s = -0.589031994 [ANSWER]
**********************
c)
Thus, getting the critical t,
df = n - 1 = 8
tcrit = - 2.896459448 [ANSWER]
***********************
d)
Reject Ho when t < -2.896 [ANSWER]
***********************
e)
As t is not less than -2.896, then we FAIL TO REJECT HO.
There is no significant evidence that the average is less than 55 s, so he shouldn't buy it.
************************
Also, the p value is
p = 0.286046498 [ANSWER]
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.