Exam 7: Introduction to Sampling Distributions

Recently the State Fish and Game planted several thousand tagged fish in a local river.The mean length of these fish,which constitute a population,is 12.6 inches.Yesterday,fishermen caught 100 of these tagged fish.You could expect that the mean length for these fish would be 12.6 inches as well since they come from the population.

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?

In order to assume that the sampling distribution for a proportion is approximately normal,the population proportion must be very close to 0.50.

A sampling distribution is the distribution of the individual values that are included in a sample from a population.

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 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?

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 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?

A sampling distribution for a sample of n = 4 is normally distributed with a standard deviation equal to 5.Based on this information,the population standard deviation,σ,is equal to 10 mph.

Suppose it is known that the mean purchase price for all homes sold last year in Blacksburg,Virginia was $203,455.Recently,two studies were done on home sales prices.In the first study,a random sample of 200 homes was selected from the population.In the second study,a random sample of 60 homes was selected.Based on this information,we know that the second study would contain more sampling errors than the first study due to the smaller sample size.

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

United Manufacturing and Supply makes sprinkler valves for use in residential sprinkler systems.United supplies these valves to major companies such as Rain Bird and Nelson,who in turn sell sprinkler products to retailers.United recently entered into a contract to supply 40,000 sprinkler valves.The contract called for at least 97% of the valves to be free of defects.Before shipping the valves,United managers tested 200 randomly selected valves and found 190 defect-free valves in the sample.The managers wish to know the probability of finding 190 or fewer defect-free valves if in fact the population of 40,000 valves is 97% defect-free.The probability is:

The Fallbrook Distributing Company has a soft drink bottling plant in Plano,Texas.Based on historical records,if its filling machine is working properly,the mean fill volume per can is 12.0 ounces with a standard deviation equal to 0.13 ounce.Further,the distribution of fill amounts is known to be normally distributed.The State of Texas has a department whose job it is to check on such consumer-related processes as soft drink filling.The idea is to protect the consumer.The department arrives at the Fallbrook plant once a month on an unscheduled day.When they arrive,they randomly select n = 4 cans and carefully measure the volume in each can.If any of these cans contains less than 11.85 ounces,the plant is shut down until a full inspection of the filling process is performed.Based on this information,the probability that the plant will get shut down if it is operating properly is approximately 0.1251.

Suppose that a population is known to be normally distributed with mean = 2,000 and standard deviation = 230.If a random sample of size n = 8 is selected,calculate the probability that the sample mean will exceed 2,100.

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

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 a single battery randomly selected from the population will have a life between 70 and 80 hours?

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.If a sample of size n = 16 turn times was selected at random from the population,the chances of the mean of this sample exceeding 20 minutes is 0.2327.

Sampling error occurs when the population parameter and the sample statistic are different.

Hillman Management Services manages apartment complexes in Tulsa,Oklahoma.They currently have 30 units available for rent.The monthly rental prices (in dollars)for this population of 30 units are: What is the range of possible sampling error if a random sample of size n = 6 is selected from the population?

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 ounce.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 ounce.