Question

For the two-sided test of H0: p = 0.21 using a sample of n = 57, how large a sample is needed to detect a proportion of 0.31 in the true population at α = 0.05 (two sided) with 90% power?

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p =0.21

Ha : p 0.21

n =57

= 0.31

P0 = 0.21

1 - P0 = 1 - 0.21 = 0.79

Test statistic = z

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

= 0.31-0.21/ [(0.21*0.79) /57 ]

= 1.85

Test statistic = z =1.85

P(z > 1.85) = 1 - P(z < 1.85) = 1 - 0.9678

P-value = 2 *0.0322 =0.0644

= 0.05

P-value >

0.0644 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that