Question

16)Conduct the following test at the alphaequals0.05 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 p 1 not equals p 2. Sample data are x 1 equals 28​, n 1 equals 254​, x 2 equals 38​, and n 2 equals 301. ​(a) Determine the null and alternative hypotheses. Choose the correct answer below. A. Upper H 0 : p 1 equals p 2 versus Upper H 1 : p 1 not equals p 2 B. Upper H 0 : p 1 equals 0 versus Upper H 1 : p 1 equals 0 C. Upper H 0 : p 1 equals p 2 versus Upper H 1 : p 1 less than p 2 D. Upper H 0 : p 1 equals p 2 versus Upper H 1 : p 1 greater than p 2 ​(b) The test statistic z 0 is nothing. ​(Round to two decimal places as​ needed.) ​(c) The​ P-value is nothing. ​(Round to three decimal places as​ needed.) Test the null hypothesis. Choose the correct conclusion below. A. Reject the null hypothesis because there is sufficient evidence to conclude that p 1 not equals p 2. B. Do not reject the null hypothesis because there is sufficient evidence to conclude that p 1 greater than p 2. C. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p 1 not equals p 2. D. Reject the null hypothesis because there is not sufficient evidence to conclude that p 1 less than p 2. Click to select your answer(s).

Answer 1

we have to test whether proportions are equal or not. So, it is a two tailed hypothesis test

(A)

(B) Using TI 84 calculator

press stat then tests then 2-propztest

enter the data

x 1 equals 28​, n 1 equals 254​, x 2 equals 38​, and n 2 equals 301

p1 not equal to p2

press calculate

we get

test statistic = -0.58

(c) p value = 0.562

We failed to reject the null hypothesis because the p value is greater than significance level0.05.

C. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p 1 not equals p 2