Accurate Confidence Intervals for a Proportion

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Accurate confidence intervals for proportion

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Question 1

104

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?

Go ahead and use the large sample confidence interval for p.

Use a plus four interval to estimate p.

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.

Question 2

154

Question 2.

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

n \geq 10

$n \geq 10$

How large depends on the value of p.

n \geq 30

$n \geq 30$

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.

Question 3

225

Question 3.

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

The proportion of a sample of 26 patients with warts who got rid of them using duct tape

The proportion of all patients with warts who could get rid of them using duct tape

The mean number of a sample of 26 with warts who got rid of them using duct tape

The mean number of all patients with warts who could get rid of them using duct tape

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.

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Question 4

264

Question 4.

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

0.27

0.23

0.85

0.80

Incorrect.

\tilde{p}

$\widetilde{p}$ =

\frac{c o u n t o f s u c c e s s + 2}{n + 4}

$\frac{count \, of \, success \,+ \, 2}{n+4}$ =

\frac{22 + 2}{26 + 4}

$\frac{22+2}{26+4}$ =

\frac{24}{30}

$\frac{24}{30}$ = 0.80

Correct.

\tilde{p}

$\widetilde{p}$ =

\frac{c o u n t o f s u c c e s s + 2}{n + 4}

$\frac{count \, of \, success \, + \,2}{n+4}$ =

\frac{22 + 2}{26 + 4}

$\frac{22+2}{26+4}$ =

\frac{24}{30}

$\frac{24}{30}$ = 0.80

Incorrect. Try again.

Question 5

350

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?

Yes

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.

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StatTutor Lesson - Accurate Confidence Intervals for a Proportion

Question 1

Question 1.

Question 2

Question 2.

Question 3

Question 3.

Question 4

Question 4.

Question 5

Question 5.