Exam 7: Introduction to Sampling Distributions

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?

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:

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

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?

A company has determined that the mean number of days it takes to collect on its accounts receivable is 36 with a standard deviation of 11 days. The company plans to select a random sample of n = 12 accounts and compute the sample mean. Which of the following statements holds true in this situation?

Suppose a population is normally distributed with a mean 100 and a standard deviation of 15. When a sample of size n = 36 is collected a sampling distribution is created. Explain which is larger: the probability of a value randomly selected from the population being larger than 120, or the probability of a sample mean being larger than 120.

If a random sample of 200 items is taken from a population in which the proportion of items having a desired attribute is p = 0.30, what is the probability that the proportion of successes in the sample will be less than or equal to 0.27?

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

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

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?

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?

Sampling error is the difference between the sample statistic and the population parameter.

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 greater than 2.

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 sample of 25 observations is taken to estimate a population proportion π. The sampling distribution of sample proportion p is:

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?

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

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

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

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 16 randomly sampled batteries from the population will have a sample mean life of between 70 and 80 hours?