A hospital is interested in studying the average number of p

A hospital is interested in studying the average number of pairs of latex

gloves that employees use per week. A random sample of 46 employees was selected and

each employee was asked how many pairs of latex gloves they used in a week. The sample

produced a mean of 22.3. Also, suppose it is known that the standard deviation is 11.9. Test

the hypothesis that the mean number of gloves the workers use in a week is greater than 20

pairs.

(a) State H_o and H_A.

(b) Find and sketch the rejection region using = 0.1

(c) Calculate the value of the test statistic and find the p-value of the test.

(d) What is your conclusion?

Solution

a)
Set Up Hypothesis
Null; number of gloves the workers use in a week is similar H0: U=20
Alternate; number of gloves the workers use in a week is greater than 20 H1: U>20
b)
Critical Value
The Value of Z at LOS 0.1% is 1.28, i.e Z > 1.28 Reject Ho
c)
Test Statistic
Population Mean(U)=20
Given That X(Mean)=22.3
Standard Deviation(S.D)=11.9
Number (n)=46
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=22.3-20/(11.9/Sqrt(46)
Zo =1.3109
| Zo | =1.3109
Critical Value
The Value of |Z | at LOS 0.1% is 1.28
We got |Zo| =1.3109 & | Z | =1.28
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Right Tail - Ha : ( P > 1.3109 ) = 0.095
Hence Value of P0.1 > 0.095, Here we Reject Ho
d)
Mean number of gloves the workers use in a week is greater than 20