Large-Sample Confidence Intervals for Proportions

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Question 1

106

Question 1.

What do we use to estimate the population proportion?

$\widehat{p}$

$\overline{x}$

Incorrect. We use sample proportion,

$\widehat{p}$ , to estimate the population proportion, p.

Correct. We use sample proportion,

$\widehat{p}$ , to estimate the population proportion, p.

Incorrect. Try again.

Question 2

139

Question 2.

Before we use the formula $\widehat{p} \pm z \sqrt{ \frac{ \widehat{p}(1- \widehat{p}) }{n} }$ , we need to make sure sample size is large enough to apply the Central Limit Theorem. What do we check?

$n \geq 30$

$n \widehat{p} \geq 10$ and

$n(1- \widehat{p} ) \geq 10$

$n \widehat{p} \geq 15$ and

$n(1- \widehat{p} ) \geq 15$

Incorrect. We check

$n \widehat{p} \geq 15$ and

$n(1- \widehat{p} ) \geq 15$ ; we cannot check

$np \geq 10$ and

$n(1-p) \geq 10$ because we don't know the value of p.

Correct. We check

$n \widehat{p} \geq 15$ and

$n(1- \widehat{p} ) \geq 15$ ; we cannot check

$np \geq 10$ and

$n(1-p) \geq 10$ because we don't know the value of p.

Incorrect. Try again.

Question 3

172

Question 3.

What is margin of error for estimating p?

$z \sqrt{ \frac{ \widehat{p}(1- \widehat{p}) }{n} }$

$\widehat{p} \pm z \sqrt{ \frac{ \widehat{p}(1- \widehat{p}) }{n} }$

$\sqrt{ \frac{ \widehat{p}(1- \widehat{p}) }{n} }$

Incorrect. Margin of error for estimating p is

$z \sqrt{ \frac{ \widehat{p}(1- \widehat{p}) }{n} }$ .

Correct. Margin of error for estimating p is

$z \sqrt{ \frac{ \widehat{p}(1- \widehat{p}) }{n} }$

Incorrect. Try again.

Question 4

248

Question 4.

How should data be collected for a confidence interval for p to be valid?

With a stratified sample

With a multistage sample

With a simple random sample

With a convenience sample

Incorrect. Data should be collected with a simple random sample.

Correct. Data should be collected with a simple random sample.

Incorrect. Try again.

Question 5

316

Question 5.

What parameter is to be estimated with a confidence interval for p?

The proportion of all Americans who approve of President Obama's job as president

The mean number of a sample of Americans who approve of President Obama's job as president

The proportion of a sample of Americans who approve of President Obama's job as president

The mean number of all Americans who approve of President Obama's job as president

Incorrect. The parameter to be estimated is the proportion of all Americans who approve of President Obama's job as president.

Correct. The parameter to be estimated is the proportion of all Americans who approve of President Obama's job as president.

Incorrect. Try again.

Question 6

437

Question 6.

What is the name of the value 0.46?

The mean number of all Americans who approve of President Obama's job as president

The proportion of a sample of 1544 Americans who approve of President Obama's job as president

The mean number of a sample of 1544 Americans who approve of President Obama's job as president

The proportion of all Americans who approve of President Obama's job as president

Incorrect. 0.46 is a value of

$\widehat{p}$ ; it is the proportion who approve of President Obama's job as president in the sample of 1544 Americans.

Correct. 0.46 is a value of

$\widehat{p}$ ; it is the proportion who approve of President Obama's job as president in the sample of 1544 Americans.

Incorrect. Try again.

Question 7

503

Question 7.

What is the name of the value 0.025?

The sample proportion

The margin of error

The population proportion

The standard error of

$\widehat{p}$

Incorrect.

$z \sqrt{ \frac{ \widehat{p}(1- \widehat{p}) }{n} }$ =

$1.96 \sqrt{ \frac{0.46(1-0.46)}{1544} } = 0.025$ is the margin of error for estimating

$\widehat{p}$ .

Correct.

$z \sqrt{ \frac{ \widehat{p}(1- \widehat{p}) }{n} }$ =

$1.96 \sqrt{ \frac{0.46(1-0.46)}{1544} } = 0.025$ is the margin of error for estimating

$\widehat{p}$ .

Incorrect. Try again.

Question 8

543

Question 8.

When the media does not report a level of confidence, what is it usually?

80%

99%

95%

90%

Incorrect. It is usually 95%.

Correct. It is usually 95%.

Incorrect. Try again.

Questions 9-10

549

Question 9.

67% is an estimate of a parameter. What is this parameter?

The mean number of all adults in the United States who drink alcohol

The proportion of all adults in the United States who drink alcohol

The mean number of a sample of 1020 adults in the United States who drink alcohol

The proportion of a sample of 1020 adults in the United States who drink alcohol

Incorrect. 0.67 is a value of

$\widehat{p}$ ; it estimate the proportion of all adults in the United States who drink alcohol.

Correct. 0.67 is a value of

$\widehat{p}$ ; it estimate the proportion of all adults in the United States who drink alcohol.

Incorrect. Try again.

Questions 11-12

726

Question 11.

Fill in the blank: The margin of error computed here is ___________ the margin of error reported by Gallup.

the same as

greater than

less than

Incorrect. Both are the same: 0.03 or 3%.

Correct. Both are the same: 0.03 or 3%.

Incorrect. Try again.

StatTutor Lesson - Large-Sample Confidence Intervals for Proportions

Question 1

Question 1.

Question 2

Question 2.

Question 3

Question 3.

Question 4

Question 4.

Question 5

Question 5.

Question 6

Question 6.

Question 7

Question 7.

Question 8

Question 8.

Questions 9-10

Question 9.

Question 10.

Questions 11-12

Question 11.

Question 12.