An employee survey conducted by a company two years ago found that 54% of its em

Question

An employee survey conducted by a company two years ago found that 54% of its employees were concerned about future health care benefits. A random sample of 80 of these employees were asked if they were now concerned about future health care benefits. Answer the following, assuming that there has been no change in the level of concern about health care benefits compared to the survey two years ago. a. What is the standard error of the sample proportion who are concerned? b. What is the probability that the sample proportion is less than 0.50? c. What is the upper limit of the sample proportion such that only 44% of the time the sample proportion would exceed this value?

Explanation / Answer

n = 80

p = 0.54

(A)

standard error = sqrt(p*(1-p)/n) = sqrt(0.54*0.46/80) = 0.0557

(B)

P(X < 0.5) = P(z < (0.5 - 0.54)/0.0557) = P(z < -0.7181) = 0.2363

(C)

Respective z-value such that area above it is 0.44, z = 0.151

using central limit theorem,

pcap = SE*z + p = 0.0557*0.151 + 0.54 = 0.5484

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.