Exam 8: Interval Estimation

The starting salary of business students in a university is known to be normally distributed.A random sample of 18 business students results in a mean salary of $46,500 with a standard deviation of $10,200.Construct the 90% confidence interval for the mean starting salary of business students in this university.

A point estimate is a function of the random sample used to make inferences about the value of an unknown population parameter.A point estimator reflects the actual value of the point estimate derived from a given sample.

Exhibit 8-5.A sample of 2,007 American adults was asked how they viewed China,with 17% of respondents indicating "unfriendly" and 6% of respondents indicating "an enemy" (Gallup,Nov.30 - Dec.18,2011). Refer to Exhibit 8-5.Construct a 99% confidence interval of the proportion of American adults who view China as "an enemy."

The daily revenue from the sale of fried dough at a local street vendor in Boston is known to be normally distributed with a known standard deviation of $120.The revenue on each of the last 25 days is noted,and the average is computed as $550.Construct a 95% confidence interval for the population mean of the sale of fried dough by this vendor.

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.

What is the purpose of calculating a confidence interval?

The t distribution is similar to the z distribution because _________________.

What is the most typical form of a calculated confidence interval?

At a particular academically challenging high school,the average GPA of a high school senior is known to be normally distributed.After a sample of 20 seniors is taken,the average GPA is found to be 2.71 and the variance is determined to be 0.25.Find a 90% confidence interval for the population mean GPA.

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 liters when constructing a 99% confidence interval?

Exhibit 8-3.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 dollars with a standard deviation of 16 thousand dollars.Assume the distribution is normally distributed. Refer to Exhibit 8-3.Construct a 95% confidence interval for the salary of new accounting professors.Answers are in thousands of dollars.

For a given sample size and population standard deviation,which of the following is true in the interval estimation of the population mean?

A confidence interval provides a value that,with a certain measure of confidence,is the population parameter of interest.

An environmentalist is measuring the number of spotted leopard lizards in central California per acre.The environmentalist surveys six acres and finds signs of 24,26,30,27,28,and 27 lizards per acre.Construct a 95% confidence interval for the average number of leopard lizards per acre.

A budget airline wants to estimate what proportion of customers would pay $10 for in-flight wireless access.Given that the airline 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 percent for a 95% confidence interval?

In an examination of holiday spending (known to be normally distributed)of a sample of 16 holiday shoppers at a local mall,an average of $54 was spent per hour of shopping.Based on the current sample,the standard deviation is equal to $21.Find a 90% confidence interval for the population mean level of spending per hour.

Exhibit 8.1.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. Refer to Exhibit 8.1.If a 99% confidence interval is constructed instead of a 95% confidence interval for the population mean,then _____________.

Newscasters wish to predict the outcome of the next presidential election with 95% confidence and a margin of error equal to 0.08.Find the appropriate sample size to accomplish this goal.

A 90% confidence interval is constructed for the population mean.If a 95% confidence interval had been constructed instead (everything else remaining the same),the width of the interval would have been ________ and the probability of making an error would have been _________.

A student interviewing at a major company wants to know his chances of getting a job offer.He surveyed 18 alumni that had interviewed with the company and found 9 of them had received a job offer.Construct a 90% confidence interval for the population proportion.