Exam 7: Statistical Inference: Estimating a Population Mean

A random sample of 40 online retailers is selected to estimate the average price of a particular item.The average price in the sample is $1.38.Suppose you build a 99% confidence interval estimate of the average price of the item for the population of online retailers represented here.Suppose further that the interval turns out to be $1.38 ± $.20.How would you interpret your result?

Suppose you plan to build a 98% confidence interval estimate of a population mean, using a sample of size 121.You will be estimating the population standard deviation with the sample standard deviation.The appropriate t-value for your interval would be ____ which you could approximate with a z score of _______ from the normal table.

Which of the following is NOT a factor influencing the width of a confidence interval?

As sample size n increases the margin of error in an interval estimate of a population mean also increases.

You want to estimate the average GMAT score for all students who took the Logitano GMAT Preparation course during the past 2 years.You select a random sample of 100 such students from a comprehensive list of all students who took the course over the last two years and find that the average GMAT score for the sample was 1040.Suppose now you build a 95% confidence interval estimate of the average score for the population of Logitano students represented here and the interval turns out to be 1040 ± 10 points.How would you interpret your result?

Hinton Motors is testing an experimental battery-powered engine for its passenger cars.Hinton has tested the range of the engine in five different trials, recording the distance traveled in each trial before the battery needed recharging.Trial results are given in the table: Produce the 90% confidence interval of the average distance for the population represented here.Assume that the population distribution is approximately normal.Report the upper bound for your interval.

An 80% confidence interval will be twice as wide as a 40% confidence interval.

Sampling without replacement is a sampling procedure in which a population member could be included more than once in the sample.

For a sample 1000 Twitter users, Tele-Market Research reports an average age of 39.If the population standard deviation is 9.5 years, what would be the upper bound for an 80% confidence interval estimate of the mean age of all Twitter users?

Torres Electronics wants to estimate the average years of seniority for employees working for the company.The files of 49 workers are selected at random.Average seniority for those in the sample is 13.6 years.Assume you know the population standard deviation is 5.2 years.You proceed to construct a 95% confidence interval estimate of average seniority for the full population of company employees.Which, if any, of the following factors would cause you to change the upper and lower bounds by more than 1/10 of a year for the interval you would produce in the situation described above? (Consider each factor independent of the others.)

Some of the reasons for sampling rather than doing a full census (100% inspection) of an entire population include:

Which of the following is NOT true of the t distribution?

As the sample size increases, the standard error of the mean increases.

The statistical principle that guarantees a near-normal sampling distribution of the sample mean no matter what the shape of the parent population distribution is:

The number of job offers received by this year's five International Business graduates of Barlow College are shown below: Suppose you were to take all possible simple random samples of size 2 that could be selected from this graduate population and calculated the sample mean number of offers for each sample.Which one of the following graphs shows the sampling distribution of the sample mean?

In a sample survey of 68 high-tech companies, Pelham Associates reported that the average training budget per employee for companies in the sample was $894.Assume the sample was selected from a population of 1320 companies, and that the standard deviation for the sample was $446.Build a 95% confidence interval estimate of the average training budget per employee for the population of high-tech firms represented here.Now suppose you want to reduce the margin of error for the interval you produced to $20, without sacrificing confidence.How big a sample size would you recommend?

In a random sample of 341 U.S.companies, the average number of paid sick days allowed company employees was 18.65.The margin of error was reported as 1 day, at the 95% confidence level.Show the upper bound for the 95% confidence interval estimate of the average number of paid sick days allowed employees by the population of all U.S.companies.

Which of the following is NOT a factor influencing the width of a confidence interval?

A single number that is the best guess of a population parameter based on sample results is called:

Stratified sampling works best when differences between groups (strata) are small and differences within groups are large.