Conduct the following test at the alpha = 0.10 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume that the samples were obtained independently using simple random sampling. Test whether p1 not equals p2. Sample data are x1 = 28, n1 = 254, x2 = 38, and n2 = 301.

a) H0: p1 - p2 = 0

H1: p1 - p2 ≠ 0

b) z=-0.58

c) p-value = 0.562

Step-by-step explanation:

We need to determine whether p1 is not equals p2, so the null and alternative hypothesis are:

H0: p1 - p2 = 0

H1: p1 - p2 ≠ 0

Where p1 and p2 are the proportions of the population. Additionally, the proportions of the sample p1' and p2' are calculated as:

Then, the test statistic is calculated using the following equation:

Where p' is calculated as:

So, replacing the values, we get that the test statistic is:

Finally, using the standard normal table, the p-value is equal to:

The p-value is greater that the value of alpha 0.1, so we can't reject the null hypothesis and there is evidence to said that p1 and p2 are equals.

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