Respuesta :
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)
[tex]n_1 = 381[/tex]
[tex]p_1 =\frac{191}{381} = 0.5013[/tex]
[tex]n_2 =166[/tex]
[tex]p_2 = \frac{145}{166} = 0.8735[/tex]
[tex]P = \frac{n_1 p_1 + n_2 p_2 }{n_1 + n_2}[/tex]
[tex]P = \frac{191 + 145}{381+166} = 0.6143[/tex]
Q = 1 - P = 0.3857
[tex]SE =\sqrt{PQ (\frac{1}{n_1} + \frac{1}{n_2})}[/tex]
[tex] = \sqrt{0.6143 \times 0.3857 \times (\frac{1}{381} + \frac{1}{166})}[/tex]
SE = 0.0452
test statics
[tex]Z = \frac{(p_1 - p_2)}{SE}[/tex]
[tex]Z = \frac{0.5013 - 0.8735}{0.0452} = -8.2345[/tex]
[tex]\alpha = 0.05[/tex] [taken 5% significance level]
from standard z table , critical value of [tex]Z = \pm 1.96[/tex]
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
