Question

A random sample of n = 1,400 observations from a binomial population produced x = 541 successes. You wish to show that p differs from 0.4.

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

z = ??

Calculate the p-value. (Round your answer to four decimal places.)

p-value = ??

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.40

Ha : p 0.40

n = 1400

x =541

= x / n = 541 / 1400 =0.39

P0 = 0.40

1 - P0 = 1 - 0.40 =0.60

Test statistic = z

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

= 0.39-0.40/ [(0.40*0.60) / 1400]

= -0.76

Test statistic = z = -0.76

P(z < -0.76) = 0.2236

P-value = 2 * 0.2236 =0.4472