Test unit 6

1.Construct a confidence interval of the population proportion at the given level of confidence. x=860

860, n=1200, 90% confidence

The lower bound of the confidence interval is ________________.

(Round to the nearest thousandth as needed.)

The upper bound of the confidence interval is _________________

2. Compute the critical value  zα/2 that corresponds to a 83 % level of confidence.

      zα/2=

nothing

(Round to two decimal places as needed.)

3. Determine the point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample with the specified characteristic, x, for the sample size provided.

Lower =0.262, upper bounds s=0.548, n=1200

The point estimate of the population proportion is

nothing .

(Round to the nearest thousandth as needed.)

The margin of error is

nothing .

(Round to the nearest thousandth as needed.)

The number of individuals in the sample with the specified characteristic is

nothing .

4. Construct a confidence interval of the population proportion at the given level of confidence.x equals 40 comma n equals 200 comma 90 % confidencex=40, n=200, 90% confidence

The 90% confidence interval is (nothing , nothing ).

5. A national survey of 1000 adult citizens of a nation found that 21% dreaded Valentine's Day. The margin of error for the survey was 11.9 percentage points with 85% confidence. Explain what this means.

Which statement below is the best explanation?

A.There is 85% confidence that 21% of the adult citizens of the nation dreaded Valentine's Day.

B.In 85% of samples of adult citizens of the nation, the proportion that dreaded Valentine's Day is between 0.091

and 0.329.

C.There is 85% confidence that the proportion of the adult citizens of the nation that dreaded Valentine's Day is between 0.091 and 0.329.

D.There is 73.1% to 96.9% confidence that 21% of the adult citizens of the nation dreaded Valentine's Day.

6. A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.02 with 95% confidence if

(a) she uses a previous estimate of 0.48?

(b) she does not use any prior estimates?

(a)

n=nothing  

(Round up to the nearest integer.)

(b)

n=nothing  

(Round up to the nearest integer.)

7. A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 3percentage points with 90% confidence if

(a) he uses a previous estimate 26%?

(b) he does not use any prior estimates?

(a) n=

nothing

 (Round up to the nearest integer.)

(b) n=

nothing

 (Round up to the nearest integer.)

8. By how many times does the sample size have to be increased to decrease the margin of error by a factor of

1/9?

The sample size must be increased by a factor of

Nothing  to decrease the margin of error by a factor of 1/9

.

(Type a whole number.)

What is the general relationship, if any, between the sample size and the margin of error?

A.Increasing the sample size by a factor M results in the margin of error decreasing by a factor of

StartFraction 1 Over StartRoot Upper M EndRoot EndFraction

1

.

B.Increasing the sample size by a factor M results in the margin of error decreasing by a factor of

StartFraction 1 Over Upper M squared EndFraction

1/

M2

.C.Increasing the sample size by a factor M results in the margin of error decreasing by a factor of

StartFraction 1 Over Upper M EndFraction

1

M

9. Determine the t-value in each of the cases.

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Click the icon to view the table of areas under the t-distribution.

(a) Find the t-value such that the area in the right tail is 0.25

with 10

degrees of freedom.

nothing  

(Round to three decimal places as needed.)

(b) Find the t-value such that the area in the right tail is 0.10 with 18

degrees of freedom.

nothing  

(Round to three decimal places as needed.)

(c) Find the t-value such that the area left of the t-value is 0.005 with 16

degrees of freedom. [Hint: Use symmetry.]

nothing  

(Round to three decimal places as needed.)

(d) Find the critical t-value that corresponds to 70%

confidence. Assume 11

degrees of freedom.

nothing  

(Round to three decimal places as needed.)

.

11.A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 1039 people age 15 or older, the mean amount of time spent eating or drinking per day is 1.62 hours with a standard deviation of 0.57 hour. Complete parts (a) through (d) below.

(a) A histogram of time spent eating and drinking each day is skewed right. Use this result to explain why a large sample size is needed to construct a confidence interval for the mean time spent eating and drinking each day.

A.Since the distribution of time spent eating and drinking each day is not normally distributed (skewed right), the sample must be large so that the distribution of the sample mean will be approximately normal.

B.Since the distribution of time spent eating and drinking each day is normally distributed, the sample must be large so that the distribution of the sample mean will be approximately normal.

C.The distribution of the sample mean will never be approximately normal.

D.The distribution of the sample mean will always be approximately normal.

(b) In 2010, there were over 200 million people nationally age 15 or older. Explain why this, along with the fact that the data were obtained using a random sample, satisfies the requirements for constructing a confidence interval.

A.The sample size is greater than 5% of the population.

B.The sample size is greater than 10% of the population.

C.The sample size is less than 10% of the population.

D.The sample size is less than 5% of the population.

(c) Determine and interpret a 90% confidence interval for the mean amount of time Americans age 15 or older spend eating and drinking each day.

Select the correct choice below and fill in the answer boxes, if applicable, in your choice.

(Type integers or decimals rounded to three decimal places as needed. Use ascending order.)

A.

The nutritionist is 90% confident that the mean amount of time spent eating or drinking per day is between

nothing  

and

nothing  

hours.

B.The nutritionist is 90% confident that the amount of time spent eating or drinking per day for any individual is between

nothing  

and

nothing  

hours.

C.There is a 90%

probability that the mean amount of time spent eating or drinking per day is between

nothing  

and

nothing  

hours.

D.The requirements for constructing a confidence interval are not satisfied.

(d) Could the interval be used to estimate the mean amount of time a 9-year-old spends eating and drinking each day? Explain.

A.Yes; the interval is about individual time spent eating or drinking per day and can be used to find the mean amount of time a 9-year-old spends eating and drinking each day.

B.Yes; the interval is about the mean amount of time spent eating or drinking per day for people people age 15 or older and can be used to find the mean amount of time spent eating or drinking per day for 9-year-olds.

C.No; the interval is about individual time spent eating or drinking per day and cannot be used to find the mean time spent eating or drinking per day for specific age.

D.No; the interval is about people age 15 or older. The mean amount of time spent eating or drinking per day for 9-year-olds may differ.

E.A confidence interval could not be constructed in part

(c).

12. The accompanying data represent the total travel tax (in dollars) for a 3-day business trip in 8

randomly selected cities. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers. Complete parts (a) through (c) below.

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