Question

Gallup’s annual Economy and Personal Finance survey found that 54% of Americans own stock. An economist claims
that this is not true. He found that 121 of 250 randomly selected Americans owned stock. At α = 0.05, is there enough
evidence to support the economist’s claim?

Answer 1

Given population proportion p = 0.54

sample size n = 250

number of americans  Americans owned stock x = 121

= x/n = 121/250 0.484

np = x = 121 >5

n(1-p) = n-x = 129 >5

Since np and n(1-p) >5 we can use normal approximation.

Hypothesis

H0: p= 0.54

H1: p 0.54

alpha = 0.05

Critical value = Z0.025 = 1.96

Rejection criteria :- If the test statistic | Z | > 1.96 then reject H0 otherwise fail to reject H0.

Test statistic Z = = = -1.777

p - value = 2* P(Z<-1.777) = 0.076

Since |Z| < Z0.025 ( 1.96) we fail to reject the H0 and there is no significant evidence to conclude that 54% of Americans own stock is not true.