Question

Results of an industry survey in the computer software fields find that the mean number of sick days taken by employees is 9.4 per year with a standard deviation of 2.7 per years. A local computer software company feels its employees take significantly fewer sick days per year. A random sample of 15 employees is selected from the local company and attendance records are reviewed. The following data represent the number of sick days taken by these employees over the past year: 8 10 5 0 6 9 5 15 5 4 3 2 0 4 15

In addition, run an appropriate test to determine if there any evidence that the employees take fewer than 9.4 sick days per year. Run the appropriate test at 5% level of significance.

Answer 1

Given that,
population mean(u)=9.4
standard deviation, σ =2.7
sample mean, x =6.0667
number (n)=15
null, Ho: μ=9.4
alternate, H1: μ<9.4
level of significance, alpha = 0.05
from standard normal table,left tailed z alpha/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 = 6.0667-9.4/(2.7/sqrt(15)
zo = -4.7814
| zo | = 4.7814
critical value
the value of |z alpha| at los 5% is 1.645
we got |zo| =4.7814 & | z alpha | = 1.645
make decision
hence value of | zo | > | z alpha| and here we reject Ho
p-value : left tail - ha : ( p < -4.7814 ) = 0
hence value of p0.05 > 0, here we reject Ho
------------------------------------------------------------------------------
null, Ho: μ=9.4
alternate, H1: μ<9.4
test statistic: -4.7814
critical value: -1.645
decision: reject Ho
p-value: 0, evidence that the employees take fewer than 9.4 sick days per year