Conduct the following test at The =0.05 level of significance by determining (a)

Question

Conduct the following test at The =0.05 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the critical value. Assume that the samples were obtained independently using simple random sampling.
random sampling Test whether p?P2 Sample data are x' "26,n, . 254, x2·36and n2·301 O Ho Pi p2 versus Hy PP O Ho P-P2 versus H P>P (b) The test statistic Zgls(Round to wo decinal places as needed ) (c) The critical values are ± | (Round to three decimal places as needed) Test the null hypothesis Choose the comect conclusion below O Do not reject the null hypothesis O Reject the null hypothesis

Explanation / Answer

Solution:

Given that x1=28, n1=254, x2=36, and n2=301.
Test Hypothesis:
(a) Ho: p1 = p2 versus H1: p1 > p2
p1 = 28/254 = 0.11
p2 = 36/301 = 0.12

P = 28+ 36/254+ 301 = 0.12
b) z = 0.11- 0.12/sqrt[0.12*(1-0.12) *(1/254+1/301)]
= -0.36
(c) Critical value = +/- 1.964
Do not reject the null hypothesis

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