Question

Consider the hypothesis test below. Ho: P 1-2250 Ha: P 1-22 > 0 The following results are for independent samples taken from the two populations. Sample 1 Sample 2 ni = 200 n2 = 400 P1 = 0.26 P2 = 0.16 -a. What is the value of the test statistic (to 2 decimals)? b. What is the p-value (to 4 decimals)? c. With a = .05, what is your hypothesis testing conclusion? Select

Answer 1

Given that,

For sample 1 :

ni = 200,01 = 0.26

For sample 2 :

n2 = 400,p2 = 0.16

The null and alternative hypotheses are,

Ho: p1 - p20

Hap1 - p2 > 0

pooled proportion is,

1 – (200 * 0.26) + (400 * 0.16) – 0.1933 200 + 400

a) Test statistic is,

Z = 0.26 – 0.16 == 2.92 0.1933 * (1 -0.1933) * (200 + 200)

Test statistic is 2.92

b) p-value = P(Z > 2.92)= 1-P(Z < 2.92)=1 - 0.9982= 0.0018

=> p-value = 0.0018

c) Since, p-value is less than

= 0,05

Reject the null hypothesis (H_{​​​​​​0}​​​).