Question

A published report indicated that 90.5% of Canadians are mobile communication subscribers. A researcher surveyed 150 Canadians and found that 130 were subscribers. At α = 0.05, test the accuracy of the claim.

Answer 1

H0: p = 0.905

Ha: p 0.905

Sample proportion = 130 / 150 = 0.8667

Test statistics

z = - p / sqrt( p ( 1 - p) / n)

= 0.8667 - 0.905 / sqrt( 0.905 * 0.095 / 150)

= -1.60

This is test statistics value.

p-value = 2 * P( Z < z)

= 2 * P( Z < -1.60)

= 2 * 0.0548

= 0.1096

Since p-value > 0.05 significance level, we do not have sufficient evidence to reject H0.

We conclude at 0.05 level that we fail to support the claim.