A company is developing a new high performance wax for cross country Sid racing

Question

A company is developing a new high performance wax for cross country Sid 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 then 55 seconds for a former Olympic champion to test it the champion will the course 8 times the champion times(selected at random) are 59.3, 63.6, 47.9, 53.3, 46.5, 45.7, 50.4, and 44.3 seconds to complete the test course should the market the wax assume the assumptions and conditions for appropriate hypothesis testing are for the sample use 0.05 as the p-value cutoff level Choose the correct null and affirmative hypotheses below H_0: mu = 55 H_A: mu > 55 H_0: mu 55 H_A: mu = 56 H_0: mu = 55 H_a: mu

Explanation / Answer

Given that,
population mean(u)=55
sample mean, x =51.375
standard deviation, s =6.918
number (n)=8
null, Ho: =55
alternate, H1: <55
level of significance, = 0.025
from standard normal table,left tailed t /2 =2.365
since our test is left-tailed
reject Ho, if to < -2.365
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =51.375-55/(6.918/sqrt(8))
to =-1.482
| to | =1.482
critical value
the value of |t | with n-1 = 7 d.f is 2.365
we got |to| =1.482 & | t | =2.365
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :left tail - Ha : ( p < -1.4821 ) = 0.09094
hence value of p0.025 < 0.09094,here we do not reject Ho
ANSWERS
---------------
null, Ho: =55
alternate, H1: <55
test statistic: -1.482
critical value: -2.365
decision: do not reject Ho
p-value: 0.09094

Yes market the was as there is suffcient evidence to conclude the mean time is less than 55 seconds

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