Conduct a test at the a=0.01 level of significance by determining (a) the null and alternative...

We are given the following sample data and are asked to test the hypothesis that p1>p2.

a) Null hypothesis

i.e., there is no significant difference between the two sample proportions

Alternate hypothesis

(one-tailed test)

i.e., there is a significant difference between the sample proportions.

b) Test statistic under H0

The test statistic for p1 and p2 is given by the formula,

Since P is not known, we use the following formula to estimate P.

=0.47(0.4678899083 actually).

=0.53.

We also have to find p1 and p2

=0.48(0.4773662551 actually)

=0.46

Now we have all the required values to find the test statistic

=0.47(0.46499984327 actually)

c) Now we find the p-value

The p-value for the test statistic is 0.3192(from areas of standard normal distribution after subtracting the value obtained from the table at 0.47 by 1 i.e., 1-0.6808 since this is a one-tail test and normal distribution is symmetric).

d) Inference

Since p-value of 0.3192 is gretaer than significance level of 0.01, we accept or in other words fail to reject the null hypothesis.

Hence i.e., there is no significant difference between the sample proportions.