AP Statistics 3.10.C Calculating Two-Proportion Intervals

Practise constructing two-proportion confidence intervals by forming the sample-proportion difference, using an unpooled standard error, and choosing the correct z-value.

Exam points

Use the difference in sample proportions as the point estimate for p1 minus p2.
Add the two unpooled variance terms under the square root for the interval standard error.
Match the critical z-value to the requested confidence level, such as 1.960 or 2.576.

[Maximum number: 1]

Two brands of golf cart batteries, R and S, were tested to investigate whether there is a difference between the proportions of fully charged batteries that could power a golf cart for at least thirty miles. A random sample of 50 brand R batteries was selected and a random sample of 50 brand S batteries was selected. Batteries were randomly assigned to one of 100 different golf carts. Each cart was driven until the battery failed. Of the carts with brand R batteries, 40 traveled over thirty miles, and of the carts with brand S batteries, 35 traveled over thirty miles. Which of the following is a 95 percent confidence interval for the difference in the proportions of fully charged batteries that can power a golf cart for at least thirty miles for the two brands?

Statistics 2021Intl MCQ

$(0.8-0.7) \pm 1.645 \sqrt{\frac{(0.8)(0.2)}{50}+\frac{(0.7)(0.3)}{50}}$

$(0.8-0.7) \pm 1.645 \sqrt{(0.75)(0.25)\left(\frac{1}{50}+\frac{1}{50}\right)}$

$(0.8-0.7) \pm 1.645 \sqrt{\frac{(0.8)(0.2)}{50}-\frac{(0.7)(0.3)}{50}}$

$(0.8-0.7) \pm 1.960 \sqrt{\frac{(0.8)(0.2)}{50}+\frac{(0.7)(0.3)}{50}}$

$(0.8-0.7) \pm 1.960 \sqrt{(0.75)(0.25)\left(\frac{1}{50}+\frac{1}{50}\right)}$

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3.10.C—Calculate an appropriate confidence interval for the difference between two population proportions question 1