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Exam 7: Introduction to Sampling Distributions

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Question 1

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In analyzing the sampling distribution of a proportion,doubling the sample size will cut the standard deviation of the sampling distribution in half.

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One of the nation's biggest regional airlines has tracked 4,000 landings and take-offs during the past month.Treating these data as the population of interest,the company found that the average time the planes spent on the ground (called the turn time)was 17.23 minutes with a standard deviation of 3.79 minutes.Further,they determined that the distribution of turn times is normally distributed.Then,the probability that a single turn time selected at random from this population would exceed 20 minutes is approximately 0.2327.

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

If 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,which of the following would be the largest individual customer bill that you might expect to find?

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

Sampling error can be eliminated if the sampling is done properly.

In a particular city,the proportion of cars that would fail an air quality emissions test is thought to be 0.13.Given this,the probability that a random sample of n = 200 cars will have a sample proportion between 0.11 and 0.15 is approximately 0.60.

A major textbook publisher has a contract with a printing company.Part of the contract stipulates that no more than 5 percent of the pages should have any type of printing error.Suppose that the company selects a random sample of 400 pages and finds 33 that have an error.If the printer is meeting the standard,what is the probability that a sample would have 33 or more errors?

The Olsen Agricultural Company has determined that the weight of hay bales is normally distributed with a mean equal to 80 pounds and a standard deviation equal to 8 pounds.Based on this,what is the probability that the mean weight of the bales in a sample of n = 64 bales will be between 78 and 82 pounds?

A claim was recently made on national television that two of every three doctors recommend a particular pain killer.Suppose a random sample of n = 300 doctors revealed that 180 said that they would recommend the painkiller.If the TV claim is correct,what is the probability of 180 or fewer in the sample agreeing?

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 would the sampling error be if a sample including the seven values in the top row were used to compute the sample mean?

Explain what is meant by the concept of sampling distribution.

Which of the following statements is false?

A particular subdivision has 20 homes.The number of people living in each of these homes is listed as follows: Which of the following statements is true when comparing a random sample of size three homes selected from the population to a random sample of size 6 homes selected from the population?

A golf course in California has determined that the mean time it takes for a foursome to complete an 18 hole round of golf is 4 hours 35 minutes (275 minutes) with a standard deviation of 14 minutes.The time distribution is also thought to be approximately normal.Every month,the head pro at the course randomly selects a sample of 8 foursomes and monitors the time it takes them to play.Suppose the mean time that was observed for the sample last month was 4 hours 44 minutes (284 minutes) .What is the probability of seeing a sample mean this high or higher?

The Good Food chain has a contract to receive eggs from a large egg producer.The eggs come in lots of 4,000 dozen each week.The contract specifies that the rate of broken or defective eggs should not exceed 8 percent.Each time a load comes in,Good Food warehouse employees select a random sample of n = 100 eggs and check to see if they are broken or defective.If Good Food wants no more than a 0.05 chance of rejecting the shipment,what should the cut-off be in terms of proportion of broken or defective eggs so that if the proportion is that value or more,the shipment will be rejected?

Suppose it is known that the income distribution in a particular region is right-skewed and bi-modal.If bank economists are interested in estimating the mean income,which of the following is true?

If a population is not normally distributed,then the sampling distribution for the mean also cannot be 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?

A random sample of 500 customers at a large retail store was selected.These customers were asked whether they had a positive experience the last time they shopped there.Only 50 customers said that they did not have a positive experience.Thus,the population parameter for proportion of customers who did have a positive experience is .90.