BackYou want to make a confidence interval for the population proportion of people between years old who have gotten a speeding ticket in the past years. A prior study found that of people between years old have received a speeding ticket in the last year. If you want your estimate to be accurate within of the true population proportion, what is the minimum sample size needed?
If you constructed one hundred 95% confidence intervals based on one hundred different simple random samples of size n, how many of the intervals would you expect to include the unknown parameter? Assume all model requirements are satisfied.
You Explain It! Valentine’s Day A Rasmussen Reports national survey of l000 adult Americans found that 18% dreaded Valentine’s Day. The margin of error for the survey was 4.5 percentage points with 95% confidence. Explain what this means.
Which type of variable is required to construct a confidence interval for a (population proportion)?
In a survey of 2096 U.S. adults, 1740 think football teams of all levels should require players who suffer a head injury to take a set amount of time off from playing to recover. (Adapted from The Harris Poll)
d. Find the minimum sample size needed to estimate the population proportion at the 99% confidence level to ensure that the estimate is accurate within 3% of the population proportion.
Controversial Song The song “Baby It’s Cold Outside” generated much controversy because of its lyrics and tone. CBS New York conducted a survey by asking viewers to use the Internet to respond to a question asking whether that song was really too offensive to play. Among 1043 Internet users who chose to respond, 986 said that the song was not too offensive, and 57 of the respondents said that the song was too offensive.
a. Construct a 95% confidence interval estimate of the proportion of the population having the belief that the song is not too offensive.
Constructing Confidence Intervals In Exercises 13–24, assume the sample is from a normally distributed population and construct the indicated confidence intervals for (b) the population standard deviation σ. Interpret the results.
Car Batteries The reserve capacities (in hours) of 18 randomly selected automotive batteries have a sample standard deviation of 0.25 hour. Use an 80% level of confidence.
Smart Phone Apple is planning for the launch of a new and improved iPhone. The marketing team wants to know the worldwide percentage of consumers who intend to purchase the new model, so a survey is being planned. How many people must be surveyed in order to be 90% confident that the estimated percentage is within three percentage points of the true population percentage?
a. Assume that nothing is known about the worldwide percentage of consumers who intend to buy the new model.
LGBT Identification In a survey of 15,349 U.S. adults, 860 identify as lesbian, gay, bisexual, or transgender. Construct a 95% confidence interval for the population proportion of U.S. adults who identify as lesbian, gay, bisexual, or transgender. (Adapted from Gallup)
Sample Size for Proportion Find the sample size required to estimate the percentage of statistics students who take their statistics course online. Assume that we want 95% confidence that the proportion from the sample is within two percentage points of the true population percentage.
Constructing Confidence Intervals In Exercises 13–24, assume the sample is from a normally distributed population and construct the indicated confidence intervals for (a) the population variance σ^2. Interpret the results.
[APPLET] Earnings The annual earnings (in thousands of dollars) of 21 randomly selected level 1 computer hardware engineers are listed. Use a 99% level of confidence. (Adapted from Salary.com)
Bisexual Idenfitication In a survey of 692 lesbian, gay, bisexual, or transgender U.S adults, 378 said that they consider themselves bisexual. Construct a 90% confidence interval for the population proportion of lesbian, gay, bisexual, or transgender U.S. adults who consider themselves bisexual. (Adapted from Gallup)
Translating Statements In Exercises 29–34, translate the statement into a confidence interval. Approximate the level of confidence.
In a survey of 2094 U.S. adults who have used an online dating app, 57% said their personal experience with online dating was positive. The survey’s margin of error is ±3.6%. (Source: Pew Research Center)
The Process of Statistics: Metastatic Melanoma OPDIVA is a drug developed by Brystol-Meyers Squib that is meant to treat metastatic melanoma, which is the worst form of skin cancer. Survival rates for patients with this cancer are 6 to 10 months. Historically, patients with metastatic melanoma were treated with a combination of chemotherapy and dacarbazine. In clinical trials, 418 patients with metastatic melanoma were randomly assigned to either OPDIVO (n=210) by receiving 3 mg/kg by intravenous infusion every 2 weeks or dacarbazine (n=208) by receiving 1000 mg/m^2 by intravenous infusion every 3 weeks. Of the 210 patients in the OPDIVO group, 45 had survived 12 months; of the 208 patients in the dacarbazine group, 22 had survived 12 months.
d. Estimate the difference in proportion of patients who had survived 12 months in the OPDIVO group versus the dacarbazine group with 95% confidence. Interpret the interval.
E-Cigarettes A New York Times article reported that a survey conducted in 2014 included 36,000 adults, with 3.7% of them being regular users of e-cigarettes. Because e-cigarette use is relatively new, there is a need to obtain today’s usage rate. How many adults must be surveyed now if we want a confidence level of 95% and a margin of error of 1.5 percentage points?
c. Does the use of the result from the 2014 survey have much of an effect on the sample size?