Question

You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly different from 0.12. You use a significance level of α=0.001 H0:p=0.12
      H1:p≠0.12

You obtain a sample of size 312 in which there are 26 successes.

What is the test statistic for this sample? (Report answer accurate to 3 decimal places.)

What is the p-value for this sample? (Report answer accurate to 4 decimal places.)

Answer 1

Solution :

The null and alternative hypothesis is

H0 : p = 0.12

Ha : p 0.12

= x / n = 26 / 312 = 0.08

P0 = 0.12

1 - P0 = 1 - 0.12 = 0.88

Test statistic = z =

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

= 0.08 - 0.12/ [(0.12 * 0.88) / 312]

Test statistic = z = -2.174

P(z < -2.174) = 0.0149

This is the two tailed test

P-value = 2 * P(z < -2.174)

P-value = 2 * 0.0149

P-value = 0.0298