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StatTutor Lesson - Accurate Confidence Intervals for Comparing Proportions

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Accurate confidence intervals for proportion
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      Question 1

      92

      Question 1.

      Suppose we check \(n \widehat{p} \geq 15 \) and \(n(1- \widehat{p} ) \geq 15\) and one is not met. What should we do to estimate p?

      		A.
      		B.
      Incorrect. We use a plus four confidence interval whenever the sample size is not large enough to use a large sample confidence interval.
      Correct. We use a plus four confidence interval whenever the sample size is not large enough to use a large sample confidence interval.
      Incorrect. Try again.
      2

      Question 2

      116

      Question 2.

      How large a sample is necessary to use a plus four confidence interval for p?

      		A.
      		B.
      		C.
      Incorrect. Sample size greater than 10 is large enough whenever the data are collected with an SRS. Note that sample size large does not depend on the value of p.
      Correct. Sample size greater than 10 is large enough whenever the data are collected with an SRS. Note that sample size large does not depend on the value of p.
      Incorrect. Try again.
      2

      Question 3

      217

      Question 3.

      What parameter do the researchers want to estimate with a 95% conficence interval?

      		A.
      		B.
      		C.
      		D.
      Incorrect. The researchers want to estimate the proportion of all patients with warts who could get rid of them using duct tape.
      Correct. The researchers want to estimate the proportion of all patients with warts who could get rid of them using duct tape.
      Incorrect. Try again.
      2

      Question 4

      265

      Question 4.

      The formula for \(\widetilde{p}\) is \(\widetilde{p}\) = \(\frac{count of success+2}{n+4} \). What is \(\widetilde{p}\) for this example?

      		A.
      		B.
      		C.
      		D.
      Incorrect. ˜p = countofsuccess+2n+4 = 22+226+4 = 2430 = 0.80
      Correct. ˜p = countofsuccess+2n+4 = 22+226+4 = 2430 = 0.80
      Incorrect. Try again.
      2

      Question 5

      351

      Question 5.

      On the basis of the interval (0.66, 0.94) can we conclude that over half of all patients with warts could get rid of them using duct tape?

      		A.
      		B.
      Incorrect. The entire interval (0.66, 0.94) is greater than 0.5, so yes, over half of all patients who might use duct tape to get rid of their warts will be successful.
      Correct. The entire interval (0.66, 0.94) is greater than 0.5, so yes, over half of all patients who might use duct tape to get rid of their warts will be successful.
      Incorrect. Try again.
      2