Answer to Question #309185 in Statistics and Probability for Kiiiiyy

Question

a) given the following n = 74, p= 5/74,

Po = 10% or

0.10 Formulates the null and alternative hypothesis, identify the test statistic and write the critical region if Po ≠ 0.10.

b) given the following n = 60, P=50/60 , Po= 0.75.

Formulates the null and alternative hypothesis, identify the test statistic and write the critical region if Po> 0.75

Answer 1

a)

Hypotheses.

Null hypothesis:Po=0.10.

Alternative hypothesis:Po ≠ 0.10.

Test statistic.

The appropriate test statistic is the z score given by:

z = (P- Po) /$\sqrt{Po(1-Po)/n}$ 

Critical region.

Suppose we test the hypothesis at $\alpha$ =0.05, from the normal distribution table, we find that the critical value z= ±1.96 (for two tailed test). Therefore, we reject the null hypothesis if the computed test statistic Z ≤ -1.96 or if Z ≥1.96

b)

Hypotheses.

Null hypothesis:Po≤0.75

Alternative hypothesis:Po>0.75

Test statistic.

The appropriate test statistic is the z score given by:

z = (P- Po) /$\sqrt{Po(1-Po)/n}$ 

Critical region.

Suppose we test the hypothesis at $\alpha$ =0.05, from the normal distribution table, we find that the critical value z=1.645 (for one tailed test). therefore, we reject the null hypothesis if the computed test statistic Z≥1.645