Exam 7: Introduction to Sampling Distributions

In an article entitled "Fuel Economy Calculations to Be Altered," James R.Healey indicated that the government planned to change how it calculates fuel economy for new cars and trucks.This is the first modification since 1985.It is expected to lower average mileage for city driving in conventional cars from 10% to 20%.AAA has forecast that the 2008 Ford F-150 would achieve 15.7 mile per gallon (mpg).The 2008 Ford F-150 was tested by AAA members driving the vehicle themselves and was found to have an average of 14.3 mpg.Assume that the mean obtained by AAA members is the true mean for the population of 2008 Ford F-150 trucks and that the population standard deviation is 5 mpg.The current method of calculating the mpg forecasts that the 2008 F-150 will average 16.8 mpg.Determine the probability that these same 100 AAA members would average more than 16.8 mpg while testing the 2008 F-150.

It is very unlikely that a nonstatistical sample will ever provide less sampling error than a statistical sample of the same size.

Suppose the life of a particular brand of calculator battery is approximately normally distributed with a mean of 75 hours and a standard deviation of 10 hours.What is the probability that 16 randomly sampled batteries from the population will have a sample mean life of between 70 and 80 hours?

Sampling error is the difference between the sample statistic and the population parameter.

According to the most recent Labor Department data,10.5% of engineers (electrical,mechanical,civil,and industrial)were women.Suppose a random sample of 50 engineers is selected.How likely is it that the random sample of 50 engineers will contain 8 or more women in these positions?

A normally distributed population has a mean of 500 and a standard deviation of 60.Determine the probability that a random sample of size 25 selected from the population will have a sample mean greater than or equal to 515.

In a recent report,it was stated that the proportion of employees who carpool to their work is 0.14 and that the standard deviation of the sampling proportion is 0.0259.However,the report did not indicate what the sample size was.What was the sample size?

Regardless of the value of the population proportion,p,(with the obvious exceptions of p = 0 and p = 1)the sampling distribution for the sample proportion, will be approximately normally distributed providing that the sample size is large enough.

A sampling distribution for a sample mean shows the distribution of the possible values for the sample mean for a given sample size from a population.

One of the things that the Central Limit Theorem tells us is that about half of the sample means will be greater than the population mean and about half will be less.

The State Department of Weights and Measures is responsible for making sure that commercial weighing and measuring devices,such as scales,are accurate so customers and businesses are not cheated.Periodically,employees of the department go to businesses and test their scales.For example,a dairy bottles milk in 1-gallon containers.Suppose that if the filling process is working correctly,the mean volume of all gallon containers is 1.00 gallon with a standard deviation equal to 0.10 gallon.Based on this information,if the department employee selects a random sample of n = 9 containers,what is the probability that the mean volume for the sample will be greater than 1.01 gallons?

The State Department of Weights and Measures is responsible for making sure that commercial weighing and measuring devices,such as scales,are accurate so customers and businesses are not cheated.Periodically,employees of the department go to businesses and test their scales.For example,a dairy bottles milk in 1-gallon containers.Suppose that if the filling process is working correctly,the mean volume of all gallon containers is 1.00 gallon with a standard deviation equal to 0.10 gallon.The department's test process requires that they select a random sample of n = 9 containers.If the sample mean is less than 0.97 gallons,the department will fine the dairy.Based on this information,what is the probability that the dairy will get fined even when its filling process is working correctly?

If the standard error for the sampling distribution of a proportion is equal to 0.0327 and if the population proportion,p,is equal to .80,the sample size must be 150.

A company has determined that the mean number of days it takes to collect on its accounts receivable is 36 with a standard deviation of 11 days.The company plans to select a random sample of n = 12 accounts and compute the sample mean.Which of the following statements holds true in this situation?

One of the leading dot-com companies has found that the proportion of customers who come into its Web site that actually makes a purchase is 0.045.The company plans to see whether this rate still holds by selecting a random sample of 200 hits on its Web site.Given that the 0.045 rate still applies,what is the standard deviation of the sampling distribution?

SeeClear Windows makes windows for use in homes and commercial buildings.The standards for glass thickness call for the glass to average 0.375 inches with a standard deviation equal to 0.050 inch.Suppose a random sample of n = 50 windows yields a sample mean of 0.392 inches.What is the probability if the windows meet the standards?