Conduct the following test at the alpha = 0.10 level of significance by determin
ID: 3300760 • Letter: C
Question
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 critical value. Assume that the samples were obtained independently using simple random sampling. Test whether p_1 notequalto p_2. Sample data are x_1 = 30, n_1 = 254, x_2 = 38 and n_2 = 301. (a) Determine the null and alternative hypotheses. Choose the correct answer below. H_0: p_1 = p_2 versus H_1: p_1 > p_2 H_0: p_1 = p_2 versus H_1: p_1Explanation / Answer
Answer to the question below:
a. The right answer is C. H0: p1 = p2 and , Ha: p1!=p2
b. Test statistic = ?
We have the test statisitc calculated as:
Test statistic = p^1 - p^2
p^1 = x1/n1, p^2 = x2/n2
pbar = x1+x2/ n1+n2
Standardized Z value is given by : (p^1-p^2)/sqrt(pbar*pbar' * sqrt( 1/n1 +1/n2))
p1 = x1/n1 = 30/254 = .118
p2 = x2/n2 = 38/301 = .126
p1-p2 = .118-.126 = -.008
pbar = x1+x2 / n1+n2 = (30+38) / (254+301) = .123
The test statistic, z = (-.008)/(sqrt(.123*(1-.123)*((1/254)+(1/301)) = -.285
c. The critical value for alpha = .10 is 1.645
Result:
We will not reject null hypothesis for the lack of data , since our test statistic (-.285) is less than the critical value 1.645.
Hence, p1=p2 is what we conclude