A telephone company claims that 20 of its customers have at

A telephone company claims that 20% of its customers have at least two telephone lines. The company selects a random sample of 500 customers and finds that 88 have two or more telephone lines. At alpha =0.05, does the data support the company\'s claim?

Solution

Ho: p >= 0.20
Ha: p < 0.20 (claim)

This means that the telephone company claims that 20% of its customers have at least two telephone lines. So, the hypothesis is customer is greater than 20% and alternate is customers having at least two telephone lines is less than 20%.

Mean Value(observed) = 88/500 = 0.176

test statistic: z(0.176) = (0.176-0.20)/sqrt(0.20*0.80/500) = -0.02/0.0178 = -1.12

p-value = P(z < -1.12) = 0.9101? (Right tailed)

Since the p-value is greater than 5% hence we do not reject the null hypothesis.