Exam 8: Interval Estimation

The main ingredient for developing a confidence interval is the sampling distribution of the underlying statistic.

The Retail Advertising and Marketing Association would like to estimate the average amount of money that a person spends for Mother's Day with 99% confidence interval and a margin of error within plus or minus $6.Assuming the standard deviation for spending on Mother's Day is $36,the required sample size is ______.

A basketball coach wants to know how many free throws an NBA player shoots during the course of an average practice.The coach takes a random sample of 43 players and finds the average number of free throws shot per practice was 225 with a standard deviation of 35.Construct a 99% confidence interval for the average number of free throws in practice.

Professors of accountancy are in high demand at American universities.A random sample of 28 new accounting professors found the average salary was $135 thousand with a standard deviation of $16 thousand.Assume the distribution is normally distributed.Construct a 95% confidence interval for the salary of new accounting professors.Answers are in thousands of dollars.

According to a report in USAToday (February 1,2012),more and more parents are helping their young adult children get homes.Suppose eight persons in a random sample of 40 young adults who recently purchased a home in Kentucky received help from their parents.You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who received help from their parents.What is the margin of error for a 95% confidence interval for the population proportion?

If a random sample of size n is taken from a normal population with a finite variance,then the statistic follows the t_df distribution with (n −1)degrees of freedom,df.

A car dealership wants to estimate the percentage of customers who are satisfied with their customer service.Given that the car dealership has no prior knowledge of the proportion,how many customers would it have to sample to ensure a margin of error of no more than 5% for a 99% confidence interval?

Recently,six single-family homes in San Luis Obispo County in California sold at the following prices (in $1,000s): 549,449,705,529,639,609.Find a 95% confidence interval for the mean sale price in San Luis Obispo County.

What is for a 99% confidence interval of the population mean based on a sample of 25 observations?

A sample of 1,400 American households was asked if they planned to buy a new car next year.Of the respondents,34% indicated they planned to buy a new car next year.Construct a 90% confidence interval of the proportion of American households who expect to buy a new car next year.

A random sample of 130 mortgages in the state of Maryland was randomly selected.From this sample,14 were found to be delinquent on their current payment.The 98% confidence interval for the proportion based on this sample is _______.

The confidence intervals for the population proportion are generally based on ___________.

When examining the possible outcome of an election,what type of confidence interval is most suitable for estimating the current support for a candidate?

The minimum sample size n required to estimate a population mean with 95% confidence and the desired margin of error 1.5 was found to be 198.Which of the following is the approximate value of the assumed estimate of the population standard deviation?

A sample of holiday shoppers is taken randomly from a local mall to determine the average daily spending on gifts.From a preselected sample,the standard deviation was determined to be $26.You would like to construct a 95% confidence interval for the mean daily spending on all holiday spending.a.Find the appropriate sample size necessary to achieve a margin of error of $5.b.Find the appropriate sample size necessary to achieve a margin of error of $8.

Bobby does not want to be late to work again.He drives to work every morning from Oakland to San Francisco and crossing the Bay Bridge seems to take forever.He times himself crossing the bridge for seven consecutive mornings,with the resulting times of 22.34,27.54,15.26,13.56,18.57,21.22,and 19.08 minutes.Construct a 99% confidence interval from those times.

An analyst takes a random sample of 25 firms in the telecommunications industry and constructs a confidence interval for the mean return for the prior year.Holding all else constant,if he increased the sample size to 30 firms,how are the standard error of the mean and the width of the confidence interval affected?

For a given confidence level and population standard deviation σ,the width of the confidence interval for the population mean is wider,the smaller the sample size n.

Pure-bred dogs competing in shows must often meet specific height criteria to be considered to be within the breed standard.A new breed of dog,the pug-cock-a-poo,has been approved by a kennel club.The variance of pug-cock-a-poo height is known to be 2.25 inches squared.You would like to estimate the mean height of all pug-cock-a-poo breeds of dogs. a.Find the appropriate sample size to achieve a margin of error of 0.3 when maintaining a 90% level of confidence. b.Find the appropriate sample size to achieve a margin of error of 0.3 when maintaining a 95% level of confidence.

A marketing firm wants to estimate how much root beer the average teenager drinks per year.A previous study found a standard deviation of 1.12 liters.How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liter when constructing a 99% confidence interval?