A metropolitan transportation authority has set a bus mechanical reliability goa

Question

A metropolitan transportation authority has set a bus mechanical reliability goal of 3, 700bus miles. Bus mechanical reliability is measured specifically as the number of bus miles between mechanical road calls. Suppose a sample of 100 buses resulted in a sample mean of 3, 750 bus miles and a sample standard deviation of 325 bus miles. Complete parts (a) and (b) below. A: a. Is there evidence that the population mean bus miles is more than 3, 700 bus miles? (Use a 0.10 level of significance.) State the null and alternative hypotheses. B: Find the TSTAT value, the critical value and the p value. Please show how you got these numbers.

Explanation / Answer

Given that,
population mean(u)=3700
sample mean, x =3750
standard deviation, s =325
number (n)=100
null, Ho: µ=3700
alternate, H1: µ>3700
level of significance, a = 0.1
from standard normal table,right tailed t a/2 =1.29
since our test is right-tailed
reject Ho, if to > 1.29
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =3750-3700/(325/sqrt(100))
to =1.538
| to | =1.538
critical value
the value of |t a| with n-1 = 99 d.f is 1.29
we got |to| =1.538 & | t a | =1.29
make decision
hence value of | to | > | t a| and here we reject Ho
p-value :right tail - Ha : ( p > 1.5385 ) = 0.06356
hence value of p0.1 > 0.06356,here we reject Ho

ANSWERS
---------------
null, Ho: µ=3700
alternate, H1: µ>3700
test statistic: 1.538
critical value: 1.29
decision: reject Ho
p-value: 0.06356

we have enough evidence to support the claim

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