Download Confidence Intervals Review

Confidence Intervals Review
***Make sure to show the four-step process or you will NOT receive full credit.***
Proportions
1. Have efforts to promote equality for women gone far enough in the United States?
A poll on this issue by the cable network MSNBC contacted 1019 adults. A
newspaper article about the poll said, “Results have a margin of sampling error of
plus or minus 3 percentage points.” Overall, 54% of the sample (550 of 1019
people) answered “Yes.”
a. What is the point estimate?
b. What is the margin of error?
c. What is the confidence interval?
2. In a survey of 1000 adults, 230 said they were somewhat concerned or very
concerned about their taxes being audited. Find a 90% confidence interval for the
proportion adults who are concerned about being audited.
3. Of 848 children surveyed, 144 plan to join a volunteer group in the future. Find a
99% confidence interval for the proportion children who will join a volunteer
group.
4. What is the critical value z* for a 95% confidence level?
5. What is the critical value z* for a 84% confidence level?
6. You are working on Hillary Clinton’s campaign for the U.S. President. A survey
of 1000 voters finds that 570 out of 1000 believe that competence is more
important than integrity in being President of the United States. Determine a 94%
confidence interval estimate for the percentage of voters who believe competence
is more important than integrity.
7. In a recent year, 73% of first-year college students responding to a national survey
identified “being very well-off financially” as an important personal goal. A state
university finds that 132 of an SRS of 200 of its first-year students say that this
goal is important.
a. Give a 95% confidence interval for the proportion of all first-year students
at the university who would identify being well-off as an important goal.
b. Is there good evidence that the proportion of all first-year students at this
university who think being very well-off is important differs from the
national survey value?
8. If 64% of a sample of 550 shoppers leaving a shopping mall claim to have spent
over $25,
a. Determine a 99% confidence interval for the proportion of all shoppers
who spend over $25.
b. Shopping mall management claims that 75% of all shoppers spend over
$25 at their mall per trip. What does your confidence interval say about
this claim?
9. A random digit dialing telephone survey of 880 drivers asked, “Recalling the last
ten traffic lights you drove through, how many of them were red when you
entered the intersections?” Of the 880 respondents, 171 admitted that at least one
light had been red. Calculate and interpret a 90% confidence interval for the
population proportion of those respondents that ran at least one red light.
Means
10. A machine at a soft-drink bottling factory is calibrated to dispense 12 ounces of
cola into cans. A SRS of 35 cans is pulled from the line after being filled and the
contents are measured. The mean content of the 35 cans is 11.92 ounces with a
standard deviation of 0.085 ounces. Calculate and interpret a 99% confidence
interval to estimate the true mean contents of the cans being filled by this machine.
11. What is the t* critical value for finding a 90% confidence interval with a sample
size of 15 observations?
12. What sample size should be chosen to find the mean number of absences per
month for school children to within + 2% at a 95% confidence level if it is known
that the standard deviation is 1.1?
13. Acute kidney transplant rejection can occur years after the transplant. In one
study, 21 patients showed rejection when the ages of their transplant were as
follows (in years):
9
6
2
2
7
3
1
1
4
2
7
3
9
1
6
1
2
2
3
7
7
Establish a 90% confidence interval estimate for the ages of the kidney transplants that
undergo rejection.
14. A company owns 335 trucks. For a SRS of 30 of those trucks, the average yearly
road tax paid $9450 with a sample standard deviation of $1205. What is the 99%
confidence interval estimate for the total yearly road taxes paid for the 335
trucks?
15. One gallon of gasoline is put in each of 30 test autos, and the resulting mileage
figures are tabulated with sample mean of 28.5 and sample standard deviation of
1.2. Find the 95% confidence interval estimate of the mean mileage.