Exam 8: Interval Estimation

Bob's average golf score at his local course is 93.6 from a random sample of 34 rounds of golf. Assume that the population standard deviation for his golf score is 4.2. The 90% confidence interval around this sample mean is ________.

A financial analyst would like to construct a 95% confidence interval for the mean earnings of a company. The company's earnings have a standard deviation of $12 million. What is the minimum sample size required by the analyst if he wants to restrict the margin of error to $2 million?

The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. If a 99% confidence interval is constructed instead of a 95% confidence interval for the population mean, then ________.

An employee of the Bureau of Transportation Statistics has been given the task of estimating the proportion of on-time arrivals of a budget airline. A prior study has estimated this on-time arrival rate as 78.5%. What is the minimum number of arrivals this employee must include in the sample to ensure that the margin of error for a 95% confidence interval is no more than 0.05?

The personnel department of a large corporation wants to estimate the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan. A random sample of six employees reveals the following family dental expenses: $180, $260, $60, $40, $100, and $80. It is known that dental expenses follow a normal distribution. Construct a 90% confidence interval for the average family dental expenses for all employees of this corporation.

We draw a random sample of size 36 from a population with standard deviation 3.5. If the sample mean is 27, what is a 95% confidence interval for the population mean?

Confidence intervals of the population mean may be created for the cases when the population standard deviation is known or unknown. How are these two cases treated differently?

The snowfall (in inches) during the month of January in a particular geographic region is normally distributed with a standard deviation of 16.75. In the last 12 years, the sample average of snowfall is computed as 122.50. A) Construct a 90% confidence interval of the average snowfall in this region. B) Construct a 95% confidence interval of the average snowfall in this region. C) Comment on the width of the preceding confidence intervals.

It is important to know that ________ is increased when we estimate the population standard deviation with the sample standard deviation.

Which of the following is the necessary condition for creating confidence intervals for the population mean?

The t distribution table lists t_df values for selected lower-tail probabilities and degrees of freedom df.

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.

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 90% confidence interval for the salary of new accounting professors. Answers are in thousands of dollars.

A confidence interval is generally associated with a(n) ________.

The Department of Education wishes to estimate the average SAT score among U.S. high school students. How many students would they have to sample, given that the test has a known population standard deviation of 100, in order to ensure that the margin of error was no more than 20 for a 99% confidence interval?

Newscasters wish to predict the outcome of the next presidential election with 99% confidence and a margin of error equal to 0.08. Find the appropriate sample size to accomplish this goal.

The minimum sample size n required to estimate a population proportion, with 95% confidence and the assumed most conservative = 0.5, was found to be 122. Which of the following is the approximate value of the assumed desired margin of error?

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?

Candidate A is facing two opposing candidates in a mayoral election. In a recent poll of 300 residents, 153 supported her. Construct a 90% confidence interval on the population proportion for the support of candidate A in the following election.

A website advertises job openings on its website, but job seekers have to pay to access the list of job openings. The website recently completed a survey to estimate the number of days it takes to find a new job using its service. It took the last 30 customers an average of 60 days to find a job. Assume the population standard deviation is 10 days. Calculate a 95% confidence interval of the population mean number of days it takes to find a job.