The mean annual cost of automobile insurance is 939

Section 7.1-7.2

1. Consider a finite population with five elements labeled A, B, C, D, E.

a) How many possible samples of size 2 can be selected?

b) List all of the possible samples of size 2?

c) Use Excel’s RAND function to assign random numbers to the five elements and list the sample of size 2 found using these random numbers.(Include a screen shot of these values)

2. Use Excel’s RAND function to assign random numbers to the 8 baseball teams below(Include a screen shot of these numbers). List the sample of size 5 that would be used from these numbers.

New York, Baltimore, Toronto, Boston, Oakland, Texas, Anaheim, Seattle

3. Indicate which of the following situations involving sampling from a finite population and which involve sampling from an infinite population.

a) Select a sample of licensed drivers in the state of South Carolina.

b) Select a sample of boxes of cereal off the production line.

c) Select a sample of cars crossing the Golden Gate Bridge on a typical weekday.

d) Select a sample of students in a statistics course at HGTC.

e) Select a sample of the orders being processed by a mail-order firm.

Section 7.3-7.5

4. Assume a population has a mean of 200 and a standard deviation of 50. Suppose a simple random sample of size 100 is selected and is used to estimate μ.

a) What is the probability that the sample mean will be within ±5 of the population mean?

b) What is the probability that the sample mean will be within ±5 of the population mean?

5. Assume the population standard deviation is Ç = 25.

a) Compute the standard error of the mean, , for samples of size 50, 100, 150, and 200.

b) What can you say about the size of the standard error of the mean as the sample size is increased?

6. The mean annual cost of automobile insurance is $939. Assume that the standard devation is Ç = $245.

a) What is the probability that a simple random sample of automobile insurance policies will have a sample mean within $25 of the population mean for each of the following sample sizes: 30, 100, 400.

b) What is the advantage of a larger sample size when attempting to estimate the population mean?

Section 7.6

7. Assume a population proportion is 0.40. A simple random sample of size 200 will be taken and the sample proportion will be used to estimate the population proportion.

a) What is the probability that the sample proportion will be within ±0.03 of the population proportion?

b) What is the probability that the sample proportion will be within ±0.05 of the population proportion?

8. The population proportion is 0.30. What is the probability that sample proportion will be within ±0.04 of the population proportion for each of the following sample sizes?

a) n = 100

b) n = 500

c) n = 1000

d) What is the advantage of a larger sample size?

9. In 2008, the Better Business Bureau(BBB) settled 75% of complaints it received. Suppose you have been hired by the BBB to investigate the complaints it received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints it is able to settle. Assume the population proportion of complaints settled for new car dealers is 0.75.

a) Suppose you have a sample of 450 complaints. Draw a sketch of the sampling distribution of .

b) Based upon a sample of 450 complaints, what is the probability that the sample proportion is within ±0.04 of the population proportion?

c) Suppose you select a sample of only 200 complaints involving new car dealers. Draw a sketch of the sampling distribution of in this case.

d) Based upon this smaller sample of 200 complaints, what is the probability that the sample proportion is within ±0.04 of the population proportion?

e) Based on your previous results, how much precision is gained from having a larger sample of 450 over having a sample of only 200?