Question

A telephone company claims that 20% of its customers have at least 2 telephone lines. The company selects a random sample of 500 customers and finds that 88 have two or more telephone lines. If Alfa = 0.05, test the company's claim.

A telephone company claims that 20% of its customers have at least 2 telephone lines. The company selects a random sample of 500 customers and finds that 88 have two or more telephone lines. If Alfa = 0.05, test the company's claim

Answer 1

Ho :   p =    0.2                  
H1 :   p ╪   0.2       (Two tail test)

p0 = .20
n = 500
x = 88
p = x/n = 88/500 = .176
alpha = .05

Z = (p-p0)/sqrt(p0*p0'/n) = (.176-.20)/sqrt(.2*.8/500) = -1.3416

The p-value is = P(t<-1.3416) = 0.0899

The alpha = .05 for 2 tailed test, therefore, for each tail a rejection region of alpha/2 = .05/2 = .025

Now, our p-value of .0899 > .025 means that we fail to reject null hypothesis. And conclude that the claim that 20% of its customers have at least 2 telephone lines.