Question

In: Math

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

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 55.5​, 62.6​, 47.2​, 53.3​, 47.6​, 49.7​, 51.4​, and 41.2 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.

a) calculate the test statistic

b) calculate the p-value

Solutions

Expert Solution

We have for given sample,              
Population mean for given sample=55
Sample mean=50.55      
Sample standard deviation= s=6.37  
Sample size =n=   8      
              
Degree of freedom = n-1 =7  
              
a)
              
t test statistic formula is              

b) P value is = 0.0444...................by using Excel command =TDIST(ABS(-1.976),7,1)

or

0.025 < P value < 0.05


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