statistics homework

20. Medical Mutual insurance is investigating the cost of a routine office visit to family practice physicians in the Rochester, New York area. The following is a list of family practice physicians in the region. Physicians are to be randomly selected and contracted regarding their charges. The 39 physicians have been coded from 00 to 38. Also noted is whether they are in practice by themselves,(s) have a partner,(P), or are in a group practice, (GP).

A. The random numbers obtained from Appendix b.6 are 31,94,43,36,03,24,17 and 09. Which physicians should be contacted?

B. Select a random sample of four physicians using the random numbers of appendix b.6

C. A sample is to consist of every fifth physician. The number 04 is selected as the starting point. Which physicians should be contacted?

D. A sample is to consist of 2 physicians in a solo practice, two in partnership and one in a group practice. Select a sample accordingly. Explain your procedure.

24. Answer the following questions in one or two well-constructed sentences.

A. what happens to the standard error of the mean if the sample size is increased?

B. What happens to the distribution of the sample mean if the sample size is increased?

C. When using the distribution of sample means to estimate the population mean, what is the benefit of using larger samples?

32. CRA Cds inc. wants the mean lengths of the “cuts” on a cd to be 135 seconds (2 min and 15 sec). This will allow the disk jockeys to have plenty of time for commercials within each 10 minute segment. Assume the distribution of the length of cuts follows the normal distribution with a population standard deviation of 8 sec. Suppose we select a sample of 16 cuts from various cd’s sold CRA cds inc.

A. what can we say about the shape of the distribution of the sample mean?

B. what is the standard error of the mean?

C. what percent of the sample means will be greater than 140 sec?

D. what percent of the sample means will be greater than 128 seconds?

E. what percent of the sample means will be greater than 128 but less than 140?

36. A recent study by Greater Las Angela’s taxi drivers association showed that the mean fare charged for service Hermosa Beach to Las Angeles international airport is $21 and the standard deviation is 3.50. We select a sample of 15 fares.

A. what is the likelihood that the sample mean is between 20 and 23?

B. what must you assume to make the above calculation?

44. An economist uses the price of a gallon of milk as a measure of inflation. She finds that the average price is 3.50 per gallon and the population standard deviation is .33. You decide the sample 40 stores, collect their price for a gallon of milk, and compute the mean price for the sample.

A. what is the standard error of the mean I this experiment?

B. what is the probability that the sample mean is between 3.46 and 3.54?

C. what is the probability that the difference between the sample mean and the population mean is less than0.01?

D. what is the likelihood the sample mean is greater than 3.60?

28. A state meat inspector in Iowa has been given the assignment of estimating the mean net weight of packages of ground chuck labeled 3 pounds. Of course he realizes that the weights cannot be precisely 3 pounds. A sample of 36 packages reveals the mean weight to be 3.01 pounds, with a standard deviation of 0.03 pounds.

A. what is the estimated population mean?

B. Determine a 95% confidence interval for the population mean.

44. During a national debate on changes to health care, a cable news service performs an opinion poll of 500 small business owners. It shows that 65% of small business owners do not approve of the changes. Develop a 95% confidence interval for the proportion opposing health care changes. Comment on result.

50. Families USA, a monthly magazine that discusses issues related to health and health costs, surveyed 20 of its subscribers. It found that the annual health insurance premiums for a family with coverage through their employers averaged $10,979. The standard deviation of the sample was 1,000.

A. Based on the sample information, develop a 90% confidence interval for the population mean yearly premium.

B. How large a sample is needed to find the population mean within $250 at 99% confidence?

56. You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide that 95% confidence level and state that the estimated proportion must be within 2% of the population proportion. A pilot survey reveals that 5 of the 50 sampled hold two or more jobs. How many in the workforce should be interviewed to meet the requirements?

62. The Tennessee tourism institute plans to saple information center visitors entering the state to learn the fraction of visitors who plan to camp in the state. Current estimates are that 35% of visitors are campers. How large a sample would you take to estimate at 95% confidence level the population proportion with an allowable error of 2%?

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