Exam 7: Introduction to Sampling Distributions

How would you respond to a statement that says that by increasing the sample size,the amount of sampling error will be decreased?

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?

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.Suppose 100 AAA members were to test the 2008 F-150.Determine the probability that the average mpg would be at least 15.7.

A major shipping company has stated that 96 percent of all parcels are delivered on time.To check this,a random sample of n = 200 parcels were sampled.Of these,184 arrived on time.If the company's claim is correct,what is the probability of 184 or fewer parcels arriving on time?

The makers of a particular type of candy have stated that 75 percent of their sacks of candy will contain 6 ounces or more of candy.A consumer group that studies such claims recently selected a random sample of 100 sacks of this candy.Of these,70 sacks actually contained 6 ounces or more.The probability that 70 or fewer sacks would contain 6 ounces or less is approximately 0.1251.

If the mean age for all students that attend your university is 24.78 years,it would be reasonable to expect that the mean of a sample of students selected from that population would also equal 24.78 years as long at the sampling is done using sound statistical methods.

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?

Regardless of population distribution,the sampling distribution for a random variable X will be approximately normally distributed.

Given a population where the proportion of items with a desired attribute is p = 0.25,if a sample of 400 is taken,what is the probability the proportion of successes in the sample will be greater than 0.22?

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.

The branch manager for United Savings and Loan in Seaside,Virginia,has worked with her employees in an effort to reduce the waiting time for customers at the bank.Recently,she and the team concluded that average waiting time is now down to 3.5 minutes with a standard deviation equal to 1.0 minute.However,before making a statement at a managers' meeting,this branch manager wanted to double-check that the process was working as thought.To make this check,she randomly sampled 25 customers and recorded the time they had to wait.She discovered that mean wait time for this sample of customers was 4.2 minutes.Based on the team's claims about waiting time,what is the probability that a sample mean for n = 25 people would be as large or larger than 4.2 minutes?

The population of incomes in a particular community is thought to be highly right-skewed with a mean equal to $36,789 and a standard deviation equal to $2,490.Based on this,if a sample of size n = 36 is selected,the sampling distribution would have a mean equal to the population mean,but the standard deviation of the sampling distribution will be one-sixth of the population standard deviation.

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

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 random sample of 100 items is selected from a population of size 350.What is the probability that the sample mean will exceed 200 if the population mean is 195 and the population standard deviation equals 20? (Hint: Use the finite correction factor since the sample size is more than 5% of the population size. )

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

The mean of a sampling distribution would be equal to the mean of the population from which the sampling distribution is constructed.

A major automobile manufacturer has developed a new model car that it claims will average 25 mpg on the highway.A random sample of fifty of these cars was tested and they averaged 24 mpg.This means that the claim made by the auto company is incorrect.

The Dilmart Company has 8,000 parts in inventory.The mean dollar value of these parts is $10.79 with a standard deviation equal to $3.34.Suppose the inventory manager selected a random sample of n = 64 parts from the inventory and found a sample mean equal to $11.27.The probability of getting a sample mean at least as large as $11.27 is approximately 0.444.

Explain the impact of the size of the sample on the shape of the sampling distribution.