Question

Refer to the Current Allergy & Clinical Immunology (March 2004) study of latex allergy in health care workers. There is a claim that the mean number of latex gloves used per day by all hospital employees is less than 20 gloves. A sample of 46 were selected with a mean number of latex gloves used per day by all hospital employees of 19.3 and standard deviation of 11.9. Assume alpha is 0.01.

What is the rejection region?
a. z<-2.575
b. z<-2.33
c. z >2.575
d. z>2.33

Answer 1

c. z >2.575

Explanation:

Sample Mean (M): =19.3

Sample Size (n): =46

Standard Deviation (s): =11.9

Confidence Level:1-a=1-0.01=0.99

Calculation

M = 19.3

Z = 2.58

sM = √(11.92/46) = 1.75

μ = M ± Z(sM)

μ = 19.3 ± 2.58*1.75

μ = 19.3 ± 4.519

Result

M = 19.3, 99% CI [14.781, 23.819].

You can be 99% confident that the population mean (μ) falls between 14.781 and 23.819.

The rejection region is Z>2.575