Question

9. (Proportion)
An educator estimates that the dropout rate for seniors at
high schools in Ohio is equal to 19%. Last year 12 seniors from a random sample
of 200 Ohio high school seniors withdrew.
At a 10% significance level, test the
educator’s claim.

Answer 1

9)

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.19

H_a : p 0.19

n = 200

x = 12

= x / n = 12 / 200 = 0.06

P₀ = 0.19

1 - P₀ = 1 - 0.19 = 0.81

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.06 - 0.19 / [(0.19 * 0.81) / 200]

= -4.486

Test statistic = -4.486

P(z < -4.486) = 0

P-value = 2 * 0 = 0

= 0.10

P-value <

Reject the null hypothesis .

The educator’s claim is true .