Question

A random sample of n = 1,000 observations from a binomial population contained 337 successes. You wish to show that p < 0.35.

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 :

The null and alternative hypothesis is

H0 : p = 0.35

Ha : p < 0.35

= x / n = 337 / 1000 = 0.337

P0 = 0.35

1 - P0 = 1 - 0.35 = 0.65

Test statistic = z =

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

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

Test statistic = z = -0.86

This is the one tailed test

= 0.05

P( z < z ) = 0.05

= P( z < -1.65 ) = 0.05

z < -1.65