Question

A random sample of n = 1,000 observations from a binomial population contained 337 successes. You wish to show that

p < 0.35.

Given: H₀: p = 0.35 versus H_a: p < 0.35

Solve:

Calculate the appropriate test statistic. (Round your answer to two decimal places.)

z =??

Provide an α = 0.05 rejection region. (Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

z> ??

z<??

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.35

H_a : p < 0.35

= 337 / 1000 = 0.337

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.337 - 0.35 / [(0.35 * 0.65) / 1000]

= -0.86

z > None

z < -1.65