A mail-order business prides itself in its ability to fill customers\' orders in

Question

A mail-order business prides itself in its ability to fill customers' orders in less than 10 calendar days, on average. Periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. On one occasion when a sample of 60 orders was selected, the average number of days was 12.367 with a population standard deviation of 2.4 days. Assume alpha, = 0.05 State Null and Alternative hypotheses. Indicate the tail or side (Left, Right or Two-tail). Find the critical value. Calculate the test statistic. Calculate the p-value. Make a conclusion either reject or not rejecting the Null hypothesis. And interpret the results.

Explanation / Answer

Given that,
population mean(u)=12.367
standard deviation, =2.4
sample mean, x =10
number (n)=60
null, Ho: =12.367
alternate, H1: <12.367
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.645
since our test is left-tailed
reject Ho, if zo < -1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 10-12.367/(2.4/sqrt(60)
zo = -7.63946
| zo | = 7.63946
critical value
the value of |z | at los 5% is 1.645
we got |zo| =7.63946 & | z | = 1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : left tail - ha : ( p < -7.63946 ) = 0
hence value of p0.05 > 0, here we reject Ho
ANSWERS
---------------
null, Ho: =12.367
alternate, H1: <12.367
test statistic: -7.63946
critical value: -1.645
decision: reject Ho
p-value: 0

we have enough evidence to support the claim

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