At a large Midwestern university,a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen finished in the bottom third of their high school class.Admission standards at the university were tightened in 1995.In 1997,a simple random sample of 100 entering freshmen found that only 10 finished in the bottom third of their high school class.Let p₁ and p₂ be the proportions of all entering freshmen in 1993 and 1997,respectively,who graduated in the bottom third of their high school class.What is a 90% plus four confidence interval for p₁ - p₂? A)0.098 ± 0.050 B)0.098 ± 0.083 C)0.098 ± 0.099 D)0.098 ± 0.130

Question

Quizplus · Accepted Answer

We can use the two-proportion z-test to construct the confidence interval. First, we calculate the pooled proportion: p̂ = (x1 + x2) / (n1 + n2) where x1 = 20, n1 = 100 (for 1993) and x2 = 10, n2 = 100 (for 1997) p̂ = (20 + 10) / (100 + 100) = 0.15 Next, we calculate the standard error: SE = sqrt(p̂(1-p̂)(1/n1 + 1/n2)) SE = sqrt(0.15(1-0.15)(1/100 + 1/100)) = 0.038 We can then calculate the z-score for a 90% confidence interval: z = 1.645 Finally, we construct the confidence interval: (p₁ - p₂) ± z * SE 0.098 ± 1.645 * 0.038 0.098 ± 0.063 0.098 ± 0.083 Therefore, the 90% plus four confidence interval for p₁ - p₂ is 0.098 ± 0.083. The best choice is B.

At a Large Midwestern University,a Simple Random Sample of 100