Question

Of a random sample of 381 high-quality investment equity options, 191 had less than 30% debt. Of an independent sample of 166 high-risk investment equity options, 145 had less than 30% debt. Test, against a two sided alternative, the null hypothesis that the two population proportions are equal.

Answer 1

Answer:

As we have calculated Z = -8.2345 THEREFORE critical value is -1.96 hence there is significant difference ,  neglect null hypothesis.

and two population are not equal

Step-by-step explanation:

Given data:

Assuming null hypothesis be Hypothesis O (P1 = P2)

Assuming alternate hypothesis be Hypothesis A (P1 is not equal to P2)

$n_1 = 381$

$p_1 =\frac{191}{381} = 0.5013$

$n_2 =166$

$p_2 = \frac{145}{166} = 0.8735$

$P = \frac{n_1 p_1 + n_2 p_2 }{n_1 + n_2}$

$P = \frac{191 + 145}{381+166} = 0.6143$

Q = 1 - P = 0.3857

$SE =\sqrt{PQ (\frac{1}{n_1} + \frac{1}{n_2})}$

   $= \sqrt{0.6143 \times 0.3857 \times (\frac{1}{381} + \frac{1}{166})}$

SE = 0.0452

test statics

$Z = \frac{(p_1 - p_2)}{SE}$

$Z = \frac{0.5013 - 0.8735}{0.0452} = -8.2345$

$\alpha = 0.05$    [taken 5% significance level]

from standard z table , critical value of $Z = \pm 1.96$

As we have calculated Z = -8.2345 THERFORE critical value is -1.96 hence there is significant difference ,  neglect null hypothesis.

and two population are not equal