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In: Statistics and Probability

The Federal Government wants to determine if the mean number of business e-mails sent and received...

The Federal Government wants to determine if the mean number of business e-mails sent and received per business dat by its employees differed from the mean number of e-mails sent and received per day by corporate employees, which is 101.5. Suppose the department electronically collects information on the number of business e-mails sent and received on a randomly selected business day over the past year from each of 10,163 randomly selected Federal employees. Test the Federal Government's hypothesis at a level of significance of 0.01. Discuss the practical significance of the results.

Solutions

Expert Solution

Assumed values,
standard deviation, sigma =24
sample mean, x =103
Assumed values,
standard deviation, sigma =24
sample mean, x =103
Given that,
population mean(u)=101.5
number (n)=10163
null, Ho: μ=101.5
alternate, H1: μ!=101.5
level of significance, alpha = 0.01
from standard normal table, two tailed z alpha/2 =2.576
since our test is two-tailed
reject Ho, if zo < -2.576 OR if zo > 2.576
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 103-101.5/(24/sqrt(10163)
zo = 6.301
| zo | = 6.301
critical value
the value of |z alpha| at los 1% is 2.576
we got |zo| =6.301 & | z alpha | = 2.576
make decision
hence value of | zo | > | z alpha| and here we reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != 6.301 ) = 0
hence value of p0.01 > 0, here we reject Ho
ANSWERS
---------------
null, Ho: μ=101.5
alternate, H1: μ!=101.5
test statistic: 6.301
critical value: -2.576 , 2.576
decision: reject Ho
p-value: 0
we have enough evidence to support the claim that the mean number of business e-mails sent and
received per business by its employees differed from the mean number of e-mails sent and received per day by corporate employees, which is 101.5

orchestra answered 2 years ago
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