Exam 7: Introduction to Sampling Distributions

If a population standard deviation is 100,then the sampling distribution for will have a standard deviation that is less than 100 for all sample sizes equal to 2 or more.

The Central Limit Theorem is of most use to decision makers when the population is known to be normally distributed.

The Chamber of Commerce in a large Midwestern city has stated that 70 percent of all business owners in the city favor increasing the downtown parking fees.The city council has commissioned a random sample of n = 100 business owners.Of these,63 said that they favor increasing the parking fees.What is the probability of 63 or fewer favoring the idea if the Chamber's claim is correct?

A particular subdivision has 20 homes.The number of people living in each of these homes is listed as follows: If a sample of size n = 5 is selected,the largest possible sample mean is:

Taking a larger sample size will always result in less sampling error but costs more money and takes more time.

According to the local real estate board,the average number of days that homes stay on the market before selling is 78.4 with a standard deviation equal to 11 days.A prospective seller selected a random sample of 36 homes from the multiple listing service.Above what value for the sample mean should 95 percent of all possible sample means fall?

A simple random sample is selected in a manner that the each possible sample of a given size has an equal chance of being selected.

Sampling error can be eliminated if the sample size is large enough.

Indicate why the Central Limit Theorem is so important in the application of statistical analysis.

Although the concept of sampling distributions is an important concept in statistics,it is very unlikely that a decision maker will actually construct a sampling distribution in any practical business situation.

Suppose the mean of dogs a pet shop grooms each day is know to be 14.2 dogs.If a sample of n = 12 days is chosen and a total of 178 dogs are groomed during those 12 days,then the sampling error is:

The size of the sampling error that comes from a random sample depends on both the variation in the population and the size of the sample being selected.

A measure computed from the entire population is called:

Suppose the mean balance of checking accounts at Regions Bank is known to be $4320.A random sample of 10 accounts yields a total of $41,490.This means the sampling error is -$171.

The J.R.Simplot Company produces frozen French fries that are then sold to customers such as McDonald's.The "prime" line of fries has an average length of 6.00 inches with a standard deviation of 0.50 inches.To make sure that Simplot continues to meet the quality standard for "prime" fries,they plan to select a random sample of n = 100 fries each day.The quality analysts will compute the mean length for the sample.They want to establish limits on either side of the 6.00 inch mean so that the chance of the sample mean falling within the limits is 0.99.What should these limits be?

The monthly electrical utility bills of all customers for the Far East Power and Light Company are known to be distributed as a normal distribution with mean equal to $87.00 a month and standard deviation of $36.00.If a statistical sample of n = 100 customers is selected at random,what is the probability that the mean bill for those sampled will exceed $75.00?

Suppose it is known that 93 percent of all parts in an inventory of 18,900 parts are in workable order.If a sample of n = 100 parts were selected from the inventory,based on the concept of sampling distributions of proportions,it can be assumed that the sample proportion of workable parts will also be 0.93.

A sample proportion can be assumed normally distributed if n ≥ 30.

The population of soft drink cans filled by a particular machine is known to be normally distributed with a mean equal to 12 ounces and a standard deviation equal to .25 ounces.Given this information,the sampling distribution for a random sample of n = 25 cans will also be normally distributed with a mean equal to 12 ounces and a standard deviation equal to .05 ounces.

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?