STEP 1: Null Hypothesis H0: P1 = P2 Alternate Hypothesis Ha: P1 ? P2 STEP 2: Analysis Plan for significance level: 0.05 STEP 3: Analyze Sample Data n1: Group 1 sample size = 400 n2: Group 2 sample size = 400 Proportion p1: = 0.0675 Proportion p2: = 0.1 Pooled Sample Proportion p = (p1 * n1 + p2 * n2) / (n1 + n2) = [(0.0675 * 400) + (0.1 * 400)] / (400 + 400) = 67 / 800 = 0.0838 Where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 2, and n2 is the size of sample 2. Standard Error: SE = sqrt{p * (1 - p ) * [(1/n1) + (1/n2)]} = sqrt{0.0838 * (1 - 0.0838 ) * [(1/400) + (1/400)]} = sqrt{0.000384} = 0.0196 STEP 4: Test Statistic z-score: z = (p1 - p2) / SE = (0.0675 - 0.1)/0.0196 = -1.659 For two-tailed test, the p-value is the probability that the z-score is less than -1.659 and more than 1.659 Use the Normal Distribution Table to find P(z < -1.659) = 0.049, and P(z >1.659) = 0.049 The Table for Standard Normal Distribution is organized as a cummulative \'area\' from the LEFT corresponding to the STANDARDIZED VARIABLE z. The Standard Normal Distribution is also symmetric (called a \'Bell Curve\') which means its an interpretive procedure to Look-Up the \'area\' from the Table. For STANDARDIZED VARIABLE z = -1.659 the corresponding LEFT \'area\' = 0.049 And due to Table\'s cummulative nature, the corresponding RIGHT \'area\' = 0.049 Solution STEP 1: Null Hypothesis H0: P1 = P2 Alternate Hypothesis Ha: P1 ? P2 STEP 2: Analysis Plan for significance level: 0.05 STEP 3: Analyze Sample Data n1: Group 1 sample size = 400 n2: Group 2 sample size = 400 Proportion p1: = 0.0675 Proportion p2: = 0.1 Pooled Sample Proportion p = (p1 * n1 + p2 * n2) / (n1 + n2) = [(0.0675 * 400) + (0.1 * 400)] / (400 + 400) = 67 / 800 = 0.0838 Where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 2, and n2 is the size of sample 2. Standard Error: SE = sqrt{p * (1 - p ) * [(1/n1) + (1/n2)]} = sqrt{0.0838 * (1 - 0.0838 ) * [(1/400) + (1/400)]} = sqrt{0.000384} = 0.0196 STEP 4: Test Statistic z-score: z = (p1 - p2) / SE = (0.0675 - 0.1)/0.0196 = -1.659 For two-tailed test, the p-value is the probability that the z-score is less than -1.659 and more than 1.659 Use the Normal Distribution Table to find P(z < -1.659) = 0.049, and P(z >1.659) = 0.049 The Table for Standard Normal Distribution is organized as a cummulative \'area\' from the LEFT corresponding to the STANDARDIZED VARIABLE z. The Standard Normal Distribution is also symmetric (called a \'Bell Curve\') which means its an interpretive procedure to Look-Up the \'area\' from the Table. For STANDARDIZED VARIABLE z = -1.659 the corresponding LEFT \'area\' = 0.049 And due to Table\'s cummulative nature, the corresponding RIGHT \'area\' = 0.049.