Question

A random sample of 430 observations produced a sample proportion equal to 0.34. Find the critical and observed values of z for the following test of hypotheses using a=0.02.

H0:p=.30 versus H1:p/=0.30 Round your answers to two decimal places.

zcritical left =_____

zcritical right =_____

zobserved =__________

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.30

H_a : p 0.30

n = 430

= 0.34

P₀ = 0.30

1 - P₀ = 1 - 0.30 = 0.70

= 0.05    

/2 = 0.025

Z/2 = Z_0.025 = 1.96

z critical left = -1.96

z critical right = 1.96

Test statistic = z =

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.34 - 0.30/ [(0.30 * 0.70) / 430]

Test statistic = z = 1.81