Exam 8: Sampling Methods and the Central Umit Theorem

Recently, a university surveyed recent graduates of the English Department for their starting Salaries. One hundred graduates returned the survey. The average salary was $35,000 with a Standard deviation of $2,000. What is the best point estimate of the population mean?

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?

The mean number of travel days per year for the outside salespeople employed by hardware Distributors is to be estimated. The 0.90 degree of confidence is to be used. The mean of a small Pilot study was 150 days, with a standard deviation of 14 days. If the population mean is to be Estimated within two days, how many outside salespeople should be sampled?

A sample of 20 is selected from the population. What is the number of degrees of freedom used to Determine the appropriate critical t-value?

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 44 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.

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.

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?

(i. The interval estimate states the range within which a population parameter probably lies. (ii. A 95 percent confidence interval implies that about 95 out of 100 similarly constructed intervals Will include the parameter being estimated. (iii) For a sampling distribution of the means, 95% percent of the means would be between ± 1.96 Standard deviations.

The following summarizes the amount of snowfall in Ontario over the past number of years. If 90% and 95% confidence intervals were developed to estimate the true average annual snowfall, What similarities would they have?

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.

i. The test statistic for a problem involving an unknown population standard deviation is the Student's t distribution. ii. The t distribution approaches the Z distribution as the sample size increases. iii. As the sample size increases, the computed value of t decreases.

(i. The interval estimate states the range within which a population parameter probably lies. (ii. The confidence interval is the interval within which a population parameter is expected to lie. (iii) For a sampling distribution of the means, 95% percent of the means would be between ± 1.96 Standard deviations.

Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for a particular Candidate. Using the 0.95 degree of confidence, what is the interval estimate for the population Proportion (to the nearest tenth of a percent)?

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.

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?

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.

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

Recently, a university surveyed recent graduates of the English Department for their starting Salaries. Four hundred graduates returned the survey. The average salary was $55,000. The Population standard deviation is known to be $2,500. What is the 90% confidence interval for the mean salary of all graduates from the English Department?

The t distribution is similar to the z distribution in all BUT ONE of the following characteristics. Which One is it?

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 98% confidence interval to estimate the true cost of a 4-litre Bag of milk?