Question

Test H₀: p= 0.5 vs H_a: p > 0.5 using a sample proportion of p^ = 0.57 and a sample size of n= 40. What is the standardized test statistic, z?

A	0.885
B	0.07
C	0.871
D	0.894

Test H₀: p= 0.5 vs H_a: p > 0.5 using a sample proportion of p^= 0.57 and a sample size of n= 40. Using your standardized test statistic from the previous question, compute the p-value for this hypothesis test.

Hint: the sign in H_a tells you to look in a specific tail of the normal distribution

A	0.284
B	0.309
C	0.025
D	0.188

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p =0.5

Ha : p > 0.5

= 0.57

P0 = 0.5

1 - P0 = 1-0.5=0.5

Test statistic = z

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

=0.57-0.5 / [(0.5*0.5) / 40]

Z= 0.885

Test statistic = z =0.885

(B)P(z > 0.885 ) = 1 - P(z < 0.885 ) = 1-0.8119=0.188

P-value = 0.188