Question

For a test of population proportion H0: p = 0.50, the z test statistic equals 1.16. Use 3 decimal places.

(a) What is the p-value for Ha: p > 0.50?

(b) What is the p-value for Ha: p ≠ 0.50?

(c) What is the p-value for Ha: p < 0.50? (Hint: The p-values for the two possible one-sided tests must sum to 1.)

(d) Which of the p-values give strong evidence against H0? Select all that apply.

The p-value in (a).

The p-value in (b).

The p-value in (c).

None of the p-values give strong evidence against H0.

Answer 1

a) The p-value for Ha: p > 0.50 $=P(Z>1.16)= 1 - P(Z\leq 1.16) = 1 - \Phi(1.16) = 1 - 0.876976 = 0.123024$

b) The p-value for Ha: p ≠ 0.50

$=P(|Z|>1.16)=2*P(Z>1.16)= 2[1 - P(Z\leq 1.16) ]= 2[1 - \Phi(1.16)] = 2(1 - 0.876976) = 0.246048$

c) The p-value for Ha: p < 0.50

$=P(Z< 1.16) = \Phi(1.16) =0.876976$

d) Since all p-values are significantly large ( > 0.10), so we can say

ans-> None of the p-values give strong evidence against H0.