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Conduct the following test at the a = 0.10 level of significance by determining (a) the null and alternative hypotheses (b) the test statistic (c) the critical value (d) the P-value. Assume that the samples were obtained independently using simple random sampling. (e) Test whether p1 does not equal p2. Sample data are x1 = 28, n1=254, x2 =38 and n2 =302.

Respuesta :

Answer:

Step-by-step explanation:

The given is to test comparison of two proportions

Hypotheses would be

[tex]H_o: p_1 =p_2\\H_a: p_1 \neq p_2\\[/tex]

(Two tailed hypothesis test at 10% significance level)

[tex]p_1 = \frac{28}{254} =0.1101\\p_2 = \frac{38}{302} =0.1258\\p = \frac{28+38}{254+302} =0.1187[/tex]

test statistic = [tex]\frac{p_1-p_2}{\sqrt{p(1-p)(\frac{1}{n_1} +\frac{1}{n_2}} )}[/tex]

=0.5662

p value = 0.56868

Since  p>0.10, accept H0.

there is statistical evidence to show that p1 equals p2

at 10% significant level.

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