Question

Conduct the following test at the a = 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 P1 7P2. Sample data are X7 = 30, ny = 254, X2 = 36 and n2 = 302. (a) Determine the null and alternative hypotheses. Choose the correct answer below. Ho: P1 = P2 versus Hy: P1 >P2 Ho: P1 = P2 versus Hy: P7 <P2 Ho: P1 = P2 versus H : P1 # P2 (b) The test statistic Zo is (Round to two decimal places as needed.)

Answer 1

Part a

Answer:

H₀: p₁ = p₂ versus H₁: p₁ ≠ p₂

[because we are given the claim as p₁ ≠ p₂]

Part b

The test statistic formula is given as below:

Z₀ = (P1 – P2) / sqrt(P*(1 – P)*((1/N1) + (1/N2)))

Where,

X1 = 30

X2 =36

N1 = 254

N2 = 302

P = (X1+X2)/(N1+N2) = (30 + 36)/(254+302) = 0.118705

P1 = X1/N1 = 30/254 = 0.11811

P2 = X2/N2 = 36/302 = 0.119205

Z₀ = (P1 – P2) / sqrt(P*(1 – P)*((1/N1) + (1/N2)))

Z₀ = (0.11811 - 0.119205) / sqrt(0.118705*(1 - 0.118705)*((1/254) + (1/302)))

Z₀ = -0.0011 / 0.027537

Z₀ = -0.03995

Z₀ = -0.04

The test statistic Z₀ is -0.04.