Exam 8: Estimation and Confidence Intervals

Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The average tread life was found to be 80,000 kilometres with a standard deviation of 5,600 kilometres. What is the best estimate of the average tread life in miles for the entire population of these tires?

College X is concerned about their employees making use of their email for non-business purposes. You have been approached to assist in this matter. College X decides on a 99% confidence level and state that the estimation proportion must be within 2 percent of the population proportion. A pilot survey reveals that 8 out of 50 emails sampled were not for business purposes. How many emails should be surveyed to meet your requirements?

A survey of 25 grocery stores revealed that the average price of a 4-litre bag of milk was $2.98 with a standard error of $0.10. What is the 95% confidence interval to estimate the true cost of a 4-litre bag of milk?

The sample size needed to estimate a population mean within 2 units with a 95% confidence when the population standard deviation equals 8 is

A financial analyst wanted to determine the mean annual return on mutual funds. A random sample of 60 returns shows a mean of 12%. If the population standard deviation is assumed to be 4%, estimate with 95% confidence the mean annual return on all mutual funds.

Dr. Patton is a professor of English. Recently she counted the number of misspelled works in a group of student essays. She noted the distribution of misspelled words per essay followed the normal distribution with a standard deviation of 2.44 words per essay. For her Tuesday class of 50 students, the mean number of misspelled words per essay was 6.05. Construct a 95% confidence interval for the mean number of misspelled words in the population of student essays.

Recently, a university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000. The population standard deviation is known to be $2,500. Interpret the results of the 95% confidence interval.

The Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 25 people reveals the mean yearly consumption to be 27 kg with a sample standard deviation of 9 kg. Assume a normal population. For a 95% confidence interval, what is the critical value needed?

A sample of 50 is selected from a known population of 250 elements. The population standard deviation is 15. What is the standard error of the sample means using the finite population correction factor?

The Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 16 people reveals the mean yearly consumption to be 27 kg with a sample standard deviation of 9 kg. Assume a normal population. For a 99% confidence interval, what is the critical value needed?

College X is concerned about their employees making use of their email for non-business purposes. A random sample of 400 e-mails discovered 70 messages that were not business related. The 95% Confidence interval for the population proportion is:

A survey of an urban university (population of 25,450) showed that 870 of 1,100 students sampled supported a fee increase to fund improvements to the student recreation center. Using the 95% level of confidence, what is the confidence interval?

The manager of the college cafeteria wants to estimate the mean amount spent per customer per purchase. A sample of 10 customers revealed the following amounts spent: Find the 99 percent confidence limits for the mean amount spent. Sample mean = $4.53, s = $1.00

The following summarizes the average price of Air Canada stock at the end of 20 randomly selected weeks in 2000. Determine a 98% confidence interval for the average TSE 300 stock index in 2000.

The z-value associated with a 94% level of confidence is:

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. Assuming a standard deviation of 3 hours, what is the required sample size if the error is to be less than ½ hour with a 99% level of confidence?

A statistics professor wishes to estimate the average mark on a term test for a course that has multiple sections and many students. A survey of some of the students registered for the course reveals the following results: Determine a 95% confidence interval for the term test results.

A manager of a local store wants to estimate the mean amount spent per shopping visit by customers. Summary statistics from a sample taken reveal the following: The store manager wonders whether the population mean could have been $50 or $60.

There are 2,000 eligible voters in a precinct. Despite protests from knowledgeable persons that a sample size of 500 was too large in relation to the total, the 500 selected at random were asked to indicate whether they planned to vote for the Liberal incumbent or the Conservative challenger. Of the 500 surveyed, 350 said they were going to vote for the Liberal incumbent. Using the 0.99 confidence coefficient, what are the confidence limits for the proportion that plan to vote for the Liberal incumbent?

Which statement(s) is/are correct about the t distribution?