Question

You wish to test the following claim at a significance level of α=0.02

      H0:p=0.76
      H1:p≠0.76

You obtain a sample of size 264 in which there are 221 successful observations.

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

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p =0.76

H_a : p 0.76

= x / n = 221/264=0.8371

P₀ = 0.76

1 - P₀ = 1 - 0.76=0.24

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.8371 - 0.24 / [(0.76*0.24) /264 ]

z= 2.934

test statistic for this sample =2.934

p-value=0.0033

so ,p=0.0033<0.02, it is concluded that the null hypothesis is rejected.