Conduct the following test at the alpha = 0.10 level of significance by determin

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_1

Explanation / 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

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