Find the null and alternative hypothesis. Conduct the following test at the -0.1

Question

Find the null and alternative hypothesis.

Conduct the following test at the -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+P2. Sample data are x -28, ny -254, x2-38, and n2-301 OA. Ho: P1 -0 versus Hy: p1-0 O c. Ho: p OB, Ho:p1-p2 versus H1:p1 p2 1-p2 versus HI : p.p2 (b) The test statistic zo is (Round to two decimal places as needed.) (c) The P-value is(Round to three decimal places as needed.) Test the null hypothesis. Choose the correct conclusion below. A. O B. C. D. Reject the null hypothesis because there is not sufficient evidence to conclude that p1 p2 Do not reject the null hypothesis because there is not sufficient evidence to conclude that p1 Reject the null hypothesis because there is sufficient evidence to conclude that pl 2 2

Explanation / Answer

A) Option-C is the correct answer.

B) p1 = 28/254 = 0.11

p2 = 38/301 = 0.13

The pooled sample proportion (P) = (p1 * n1 + p2 * n2)/(n1 + n2)

= (0.11 * 254 + 0.13 * 301)/555

= 0.12

SE = sqrt (P * (1 - P) * (1/n1 + 1/n2))

= sqrt(0.12 * 0.88 * (1/254 + 1/301))

= 0.03

The test statistic Z = (p1 - p2)/SE

= (0.11 - 0.13)/0.03

= -0.67

C) p-value = 2 * P(Z < -0.67)

= 2 * 0.2514

= 0.5028

As the p-value is greater than the test statistic value, SO the null hypothesis is not rejected.

Option-C is the correct answer.

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