Question

Suppose we want to test the null hypothesis H0 : p = 0.28 against the alternative hypothesis H1 : p ≠ 0.28. Suppose also that we observed 100 successes in a random sample of 400 subjects and the level of significance is 0.05. What are the critical values for this test?

a. -1.96 and 1.96

b. 0.05 and 0.01

c. -1.39 and 1.39

d. -1.6449 and 1.6449

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.28

H_a : p 0.28

n =

x =100

= x / n = 100/ 400 =0.25

P₀ = 0.28

1 - P₀ = 1 - 0.28 =0.72

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.25 - 0.28 / [0.28 *0.72 /400 ]

= −1.336

Test statistic = z = −1.34

P-value = 0.1814

= 0.05

P-value ≥

0.1814  ≥ 0.05

Do not reject the null hypothesis .

There is insufficient evidence to suggest that  

The significance level is α=0.05, and the critical value for a two-tailed test is z_c​=1.96.

The rejection region for this two-tailed test is - 1.96. and 1.96.

Option a ) is correct.