In a random sample of n1 = 162 males, there are x1 = 63 people that have blue eyes. In a random sample of n2 = 333 females, there are x2 = 97 that have blue eyes. The researcher would like to test the hypothesis that the percent of males with blue eyes is different than the percent of females that have blue eyes. Given a level of significance of alpha=0.05, what are the critical values for the test of hypothesis?

z = 2.1784 > 1.96,

Reject the null hypothesis

Step-by-step explanation:

For the males:

n1  = 162, x1 = 63

P1 = x 1/ n1 = 0.3889

For the Females:

n2 = 333,

x2 = 97

P 2 = x2/n2

= 0.2913

P 1= P2 Null hypothesis

P 1 is not equal to P 2 alternative hypothesis

Pooled proportion:

P= (x1 + x2) /( n1+ n2)

= (63 + 97) / (162 + 333)= 0.3232

Test statistics :

Z= (p1 - p2) /√p(1-p)× (1/n1 + 1/n2)

0.3889- 0.2913 / √0.3232 × 0.6768 × (1/162 +1/333)

=2.1784

c) Critical value :

Two tailed critical value, z critical = Norm.S .INV (0.05/2) = 1.960

Reject H o if z < -1.96 or if z > 1.96

d) Decision:

z = 2.1784 > 1.96,

Reject the null hypothesis