Question

Independent random samples of sizes n₁ = 202 and n₂ = 210 were taken from two populations. In the first sample, 170 of the individuals met a certain criteria whereas in the second sample, 178 of the individuals met the same criteria.

Test the null hypothesis H0:p1=p2versus the alternative hypothesis HA:p1>p2.

a)  Calculate the z test statistic, testing the null hypothesis that the population proportions are equal.

Round your response to at least 3 decimal places.

    

b) What is the approximate value of the p-value?

Round your response to at least 3 decimal places.

   

c)  Is there any evidence, at the 10% level of significance, to indicate that p₁and p₂are not equal to each other?    

Answer 1

Solution-

a) Test Statistic

Z = - 0.169

b) P- value

P = 0.5671

c) Conclusion

test results that null hypothesis is not rejected.

So, at 10% level of significance there is not enough evidence to indicate that p1 and p2 are not equal to each other.

by test result p1 and p2 are equal.