Exam 7: Introduction to Sampling Distributions

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.

A pharmaceutical company claims that only 5 percent of patients experience nausea when they take a particular drug.In a research study,n = 100 patients were given this drug and 8 experienced nausea.Assuming that the company's claim is true,what is the probability of 8 or more patients experiencing nausea?

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 inch.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 following values represent the population of home mortgage interest rates (in percents)being charged by the banks in a particular city: Given this information,what is the most extreme amount of sampling error possible if a random sample of n = 4 banks is surveyed and the mean loan rate is calculated?

A population has a proportion equal to 0.30.Calculate the following probabilities with n = 100.Find P( ≥ 0.27).

Princess Cruises recently offered a 16-day voyage from Beijing to Bangkok during the time period from May to August.The announced price,excluding airfare,for a room with an ocean view or a balcony was listed as $3,475.Cruise fares usually are quite variable due to discounting by the cruise line and travel agents.A sample of 20 passengers who purchased this cruise paid the following amounts (in dollars): Determine the sampling error for this sample.

Assume that n = 18 people are asked a yes/no survey question,and 6 people say "yes" while 12 people say "no." Based on this information the sample proportion can be assumed normally distributed.

A particular subdivision has 20 homes.The number of people living in each of these homes is listed as follows: If a random sample of n = 3 homes were selected,what would be the highest possible positive sampling error?

Princess Cruises recently offered a 16-day voyage from Beijing to Bangkok during the time period from May to August.The announced price,excluding airfare,for a room with an ocean view or a balcony was listed as $3,475.Cruise fares usually are quite variable due to discounting by the cruise line and travel agents.A sample of 20 passengers who purchased this cruise paid the following amounts (in dollars): Calculate the sample mean cruise fare.

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 will contain fewer than 5 women in these positions?

The impact on sampling of increasing the sample size is:

The sampling distribution for is actually the distribution of possible sampling error for samples of a given size selected at random from the population.

A population has a proportion equal to 0.30.Calculate the following probabilities with n = 100.Find P(0.25 < ≤ 0.40).

The size of the standard error of the sample proportion is dependent on the value of the population proportion and the closer the population proportion is to .50,the larger the standard error for a given sample size will be.

A population with a mean of 1,250 and a standard deviation of 400 is known to be highly skewed to the right.If a random sample of 64 items is selected from the population,what is the probability that the sample mean will be less than 1,325?

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 inch.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.Yesterday,the sample mean was 6.05 inches.What is the probability that the mean would be 6.05 inches or more if they are meeting the quality standards?

In a campaign speech,a candidate for governor stated that about 63 percent of the people in the state were in favor of spending additional money on higher education.After the speech,a polling agency surveyed a random sample of 400 people and found 234 people who favored more spending on higher education.Based on the candidate's statement,the probability of finding 234 or fewer is approximately 0.97.

A smaller sample might provide less sampling error than a larger sample from a given population.

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

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 gallon,the department will fine the dairy.Based on this information,suppose that the dairy wants no more than a 0.05 chance of being fined,which of the following options exist if they can't alter the filling standard deviation?