Question

A random sample of 410 observations produced a sample proportion equal to 0.37. Find the critical and observed values of z for the following test of hypotheses using a = 0.02. Ho: p = 0.30 versus H :p *0.30. Round your answers to two decimal places. Zcritical left = Z critical right Zobserved =

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.30

H_a : p $\neq$ 0.30

$\hat p$ = 0.37

P₀ = 0.30

1 - P₀ = 1 - 0.30 = 0.70

$\alpha$ = 0.02

$\alpha$/2 = 0.01

Z_$\alpha$/2 = Z_0.01 ± 2.33

z critical left = z <-2.33

z critical right = z > 2.33

Test statistic = z=

= $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

= 0.37 - 0.30/ [$\sqrt$(0.30 * 0.70) / 410 ]

Test statistic = z observed = 3.09