3. Carlton Bolden has difficulty making on-time deliveries, averaging at least 1

Question

3. Carlton Bolden has difficulty making on-time deliveries, averaging at least 16 minutes late This is printed on his annual evaluation form. He believes that it is a vehicle scheduling problem. With a schedule adjustment, he believes he can decrease his late delivery time. To challenge his present record, he makes the schedule adjustment. The next 36 deliveries he averaged 12 minutes late with a sample standard deviation of 9 minutes. At 0.05 significance level, test if he has improved his service State the null and the alternative hypotheses. Calculate the critical value (to 3 decimals). Calculate the test statistic (to 2 decimals). Using the Critical Value Approach, what decision should be made and WHY? What is the p-value (to 3 decimals)? Using the evalue Approach, what decision should be made and WHY?

Explanation / Answer

Given that,
population mean(u)=16
sample mean, x =12
standard deviation, s =9
number (n)=36
null, Ho: =16
alternate, H1: <16
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.69
since our test is left-tailed
reject Ho, if to < -1.69
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =12-16/(9/sqrt(36))
to =-2.6667
| to | =2.6667
critical value
the value of |t | with n-1 = 35 d.f is 1.69
we got |to| =2.6667 & | t | =1.69
make decision
hence value of | to | > | t | and here we reject Ho
p-value :left tail - Ha : ( p < -2.6667 ) = 0.00576
hence value of p0.05 > 0.00576,here we reject Ho
ANSWERS
---------------
null, Ho: =16
alternate, H1: <16
test statistic: -2.6667
critical value: -1.69
decision: reject Ho
p-value: 0.00576
have evidence that he has improved his service

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