Question

A telephone company claims that 20% of its customers have a landline telephone. The company selects a random sample of 500 customers and finds that 88 have a landline. At a .05 level of significance, is the company’s claim valid. Use the P-value approach. Clearly state the null and alternative hypothesis, locate the claim and state the decision.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p =0.20

Ha : p 0.20

n = 500

x = 88

= x / n = 88 / 500 = 0.18

P0 = 0.20

1 - P0 = 1 - 0.20 = 0.80

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.18 - 0.20 / [(0.20*0.80) / 500]

= -1.12

Test statistic = z = -1.12

P-value = 2 * 0.1314 =0.2628

= 0.05

P-value >

0.2628 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that