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 51.4, 63.3​, 51.2, 54.3​,49.4,49.4,50.8,and 40.3 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. Calculate the t statistic-round to three decimal places The P value is-round to three decimal places?

Answer 1

Here we have given that,

X
51.4
63.3
51.2
54.3
49.4
49.4
50.8
40.3

X: Champions time

n=number of champions =8

= sample mean == 51.26

s=sample standard deviation= 6.34

Claim: To check whether the mean time to finish their standard test course should be less than 55 seconds for a former Olympic champion

The Hypothesis is as follows

v/s

Now, we can find the test statistic

t-statistics=

=

= -1.667

we get,

the Test statistic is -1.667

Now we find the P-value

= level of significance=0.05

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

This is one left tailed test

Now, we can find the P-value

P-value =0.070 using excel = TDIST( | t-stat | = 1.667, d.f = 7, tail=1)

we get the P-value is 0.070

Decision:

P-value > 0.05 ()

That is we fail to reject reject Ho (Null Hypothesis)

Conclusion

There is the not sufficient evidence that the mean time to finish their standard test course should be less than 55 seconds for a former Olympic champion