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Confidence Intervals for Proportions Practice Questions

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Updated on Oct 5, 2011

To review these concepts, go to Confidence Intervals for Proportions Study Guide.

Confidence Intervals for Proportions Practice Questions

Practice

A law school wants to know how successful its graduates are at passing the bar exam on the first try. Two hundred graduates are randomly selected and asked whether they passed the bar exam the first time they took it. Of the 200 graduates, 130 said they passed the exam on the first try.

  1. Set a 98% confidence interval for the proportion of law student graduates at this university who passed the bar exam. Interpret the interval in the context of the problem.
  2. Give a potential source of bias in this study.

Consider the law school's study of the proportion of its graduates who pass the bar exam on the first try. Earlier, we had a sample of 200 and set a 98% confidence interval on the proportion of students who passed the bar exam on the first try.

  1. Set a 99% confidence interval for the population proportion of graduates who pass the bar exam on the first try. Compare the two intervals.
  2. Suppose that only 100 graduates were sampled and 65 reported passing the bar exam on the first try. (Note that the estimated proportion is the same for both samples.) Set a 99% confidence interval on the proportion of the school's graduates who pass the bar exam the first time. Compare the intervals.

Solutions

  1. Confidence interval = (0.57, 0.73)
  2. Response bias; people who didn't pass could have been embarrassed and said they did pass.
  3. A 99% confidence interval = (0.56,0.76), compared to a 98% confidence interval of (0.57,0.73). Clearly, the 99% confidence interval is wider. This makes sense because, as the interval increases in length, we become more confident that the interval will capture the true population proportion.
  4. A 99% confidence interval = (0.54,0.76). As the sample size decreased, the confidence interval widened.
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