Question

3) You are asked the conduct the following hypothesis test concerning a population proportion:

H₀: prop = 0.82

H_A: prop ≠ 0.82

You draw a sample of size 1,024 from the population. There are 850 individuals in the sample who satisfy the criteria in which we are interested. Calculate the p-value for this test.

Round your answer to 4 decimal places.

Answer 1

Solution :

Given that,

= 0.82

1 - = 0.18

n = 1024

x = 850

Point estimate = sample proportion = = x / n = 0.830

This a two- tailed test.

Test statistics

z = ( - ) / *(1-) / n

= ( 0.830 - 0.82) / (0.82*0.18) / 1024

= 0.839

P-value = 2 * P(Z>z)

= 2 * (1 - P(Z <z ))

= 2 * (1- P(Z < 0.839) )

= 2 * (1 - 0.7993 )

= 0.4010

The p-value for this test is 0.4010.