Exam 8: Estimation and Confidence Intervals

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. If 90% and 95% confidence intervals were developed to estimate the true cost of a 4-litre bag of milk, what similarities would they have?

i. The t distribution is based on the assumption that the population of interest is normal or nearly normal. Ii) The t distribution is a discrete distribution. Iii) There is not one t distribution, but rather a "family" of t distributions.

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. Develop a 90% confidence interval for the mean annual consumption of sugar.

A 95 percent confidence interval implies that about 95 out of 100 similarly constructed intervals will include the ________being estimated.

How large a sample of government employees should be taken if we want to estimate with 98% confidence the mean salary to within $2,000? The population standard deviation is assumed to be $10,500. (Round up to the nearest whole number)

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. Develop a 99% confidence interval for the mean annual consumption of sugar.

College X is concerned about their employees making use of their email for non-business purposes. A random sample of 400 e-mails discovered 80 messages that were not business related. The 90% Confidence interval for the population proportion is:

7 years. What is the 95% confidence interval for the true population mean?

A sample of 100 students is selected from a known population of 1,000 students to construct a 95% confidence interval for the average SAT score. What correction factor should be used to compute the standard error?

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 98% confidence interval for the term test results.

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 with a standard deviation of $2,500. What is the best point estimate of the population mean?

i. The higher the degree of confidence, the larger the sample required to give a certain precision. ii. To determine the size of a sample, the standard deviation of the population must be estimated by either taking a pilot survey or by approximating it based on knowledge of the population. Iii) One factor in determining the size of a sample is the maximum allowable error that you must decide on. It is the maximum error you will tolerate at a specified level of confidence.

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 90% confidence level and state that the estimation proportion must be within 2 percent of the population proportion. A pilot survey reveals that 10 out of 50 emails sampled were not for business purposes. How many emails should be surveyed to meet your requirements?

A survey of 144 retail stores revealed that the average price of a DVD was $375 with a standard error of $20. If 95% and 98% confidence intervals were developed to estimate the true cost of the DVD, what differences would they have?

A bank wishes to estimate the mean balances owed by customers holding MasterCard. The population standard deviation is estimated to be $300. If a 98 percent confidence interval is used and an interval of $75 is desired, how many cardholders should be sampled?

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 90% confidence interval for the mean number of misspelled words in the population of student essays.

The following summarizes the amount of snowfall in Ontario over the past number of years. You wonder whether the population mean could have been 2000 or 1900.

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. Develop a 95% confidence interval for the mean annual consumption of sugar.

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 90% 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 sample of 500 executives who own their own home revealed 175 planned to sell their homes and retire to Victoria. Develop a 98% confidence interval for the proportion of executives that plan to sell and move to Victoria.