# When using the distribution of sample means to estimate the population mean, what is the benefit of using larger sample sizes?

Unit 1 Homework Instructions Directions

Complete the following questions from Chapter 8 and 9. Use textbook as only reference. Some questions have additional data or excel sheet attached to this order.

Chapter 8

• In chapter exercises: Problems 2, 10, and 18, in Connect.
• End of chapter exercises: Problems 24, and 42, in Connect.
• End of chapter Data Set Exercise 46. Show all your work and calculations.

Chapter 9

• In chapter exercises: Problems 2, 14, and 26, in Connect.
• End of chapter exercises: Problems 32, 44, 52, and 62, in Connect.
• End of chapter Data Set Exercise 64. Show all your work and calculations.

Chapter 8 Questions:

In chapter exercises:

Question 2:

The following is a list of hospitals in the Cincinnati (Ohio) and Northern Kentucky Region. Also included is whether the hospital is a general medical/surgical hospital (M/S) or a specialty hospital (S). We are interested in estimating the average number of full- and part-time nurses employed in the area hospitals.

1. A sample of five hospitals is to be randomly selected. The random numbers are 09, 16, 00, 49, 54, 12, and 04. Which hospitals are included in the sample?
2. Use a table of random numbers to develop your own sample of five hospitals.
 ID Number Name Address Type 00 Bethesda North 10500 Montgomery Cincinnati, Ohio 45242 M/S 01 Ft. Hamilton-Hughes 630 Eaton Avenue Hamilton, Ohio 45013 M/S 02 Jewish Hospital-Kenwood 4700 East Galbraith Rd. Cincinnati, Ohio 45236 M/S 03 Mercy Hospital-Fairfield 3000 Mack Road Fairfield, Ohio 45014 M/S 04 Mercy Hospital-Hamilton 100 Riverfront Plaza Hamilton, Ohio 45011 M/S 05 Middletown Regional 105 McKnight Drive Middletown, Ohio 45044 M/S 06 Clermont Mercy Hospital 3000 Hospital Drive Batavia, Ohio 45103 M/S 07 Mercy Hospital-Anderson 7500 State Road Cincinnati, Ohio 45255 M/S 08 Bethesda Oak Hospital 619 Oak Street Cincinnati, Ohio 45206 M/S 09 Children’s Hospital Medical Center 3333 Burnet Avenue Cincinnati, Ohio 45229 M/S 10 Christ Hospital 2139 Auburn Avenue Cincinnati, Ohio 45219 M/S 11 Deaconess Hospital 311 Straight Street Cincinnati, Ohio 45219 M/S 12 Good Samaritan Hospital 375 Dixmyth Avenue Cincinnati, Ohio 45220 M/S 13 Jewish Hospital 3200 Burnet Avenue Cincinnati, Ohio 45229 M/S 14 University Hospital 234 Goodman Street Cincinnati, Ohio 45267 M/S 15 Providence Hospital 2446 Kipling Avenue Cincinnati, Ohio 45239 M/S 16 St. Francis-St. George Hospital 3131 Queen City Avenue Cincinnati, Ohio 45238 M/S 17 St. Elizabeth Medical Center, North Unit 401 E. 20th Street Covington, Kentucky 41014 M/S 18 St. Elizabeth Medical Center, South Unit One Medical Village Edgewood, Kentucky 41017 M/S 19 St. Luke’s Hospital West 7380 Turfway Drive Florence, Kentucky 41075 M/S 20 St. Luke’s Hospital East 85 North Grand Avenue Ft. Thomas, Kentucky 41042 M/S 21 Care Unit Hospital 3156 Glenmore Avenue Cincinnati, Ohio 45211 S 22 Emerson Behavioral Science 2446 Kipling Avenue Cincinnati, Ohio 45239 S 23 Pauline Warfield Lewis Center for Psychiatric Treat. 1101 Summit Road Cincinnati, Ohio 45237 S 24 Children’s Psychiatric No. Kentucky 502 Farrell Drive Covington, Kentucky 41011 S 25 Drake Center Rehab—Long Term 151 W. Galbraith Road Cincinnati, Ohio 45216 S 26 No. Kentucky Rehab Hospital—Short Term 201 Medical Village Edgewood, Kentucky S 27 Shriners Burns Institute 3229 Burnet Avenue Cincinnati, Ohio 45229 S 28 VA Medical Center Cincinnati, Ohio 45220 3200 Vine S

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1. A sample is to consist of every fifth location. We select 02 as the starting point. Which hospitals will be included in the sample?
2. A sample is to consist of four medical and surgical hospitals and one specialty hospital. Select an appropriate sample.

Question 10:

There are five sales associates at Mid-Motors Ford. The five representatives and the number of cars they sold last week are:

 Sales Representative Cars Sold Peter Hankish 8 Connie Stallter 6 Juan Lopez 4 Ted Barnes 10 Peggy Chu 6
1. How many different samples of size 2 are possible?
2. List all possible samples of size 2, and compute the mean of each sample.
3. Compare the mean of the sampling distribution of sample means with that of the population.
4. On a chart similar to CHART 8–1, compare the dispersion in sample means with that of the population.

Question 18:

According to an IRS study, it takes a mean of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form. This distribution of times follows the normal distribution and the standard deviation is 80 minutes. A consumer watchdog agency selects a random sample of 40 taxpayers.

1. What is the standard error of the mean in this example?
2. What is the likelihood the sample mean is greater than 320 minutes?
3. What is the likelihood the sample mean is between 320 and 350 minutes?
4. What is the likelihood the sample mean is greater than 350 minutes?

End of chapter exercises:

Question 24:

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

1. What happens to the standard error of the mean if the sample size is increased?

Page 250

1. What happens to the distribution of the sample means if the sample size is increased?
2. When using the distribution of sample means to estimate the population mean, what is the benefit of using larger sample sizes?

Question 42:

Human Resource Consulting (HRC) surveyed a random sample of 60 Twin Cities construction companies to find information on the costs of their health care plans. One of the items being tracked is the annual deductible that employees must pay. The Minnesota Department of Labor reports that historically the mean deductible amount per employee is \$502 with a standard deviation of \$100.

1. Compute the standard error of the sample mean for HRC.
2. What is the chance HRC finds a sample mean between \$477 and \$527?
3. Calculate the likelihood that the sample mean is between \$492 and \$512.
4. What is the probability the sample mean is greater than \$550?

End of chapter Data Set Exercise (show all calculations):

Question 46:

Refer to the Real Estate data (Attached to this order), which report information on the homes sold in the Goodyear, Arizona, area last year. Use statistical software to compute the mean and the standard deviation of the selling prices. Assume this to be the population. Select a sample of 10 homes. Compute the mean and the standard deviation of the sample. Determine the likelihood of a sample mean this large or larger from the population.

Chapter 9 Questions:

In chapter exercises:

Question 2:

A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 95% confidence interval for the population mean.

Question 14:

The Greater Pittsburgh Area Chamber of Commerce wants to estimate the mean time workers who are employed in the downtown area spend getting to work. A sample of 15 workers reveals the following number of minutes spent traveling.

 29 38 38 33 38 21 45 34 40 37 37 42 30 29 35

Develop a 98% confidence interval for the population mean. Interpret the result.

(Excel document for this question attached to this order)

Question 26:

Past surveys reveal that 30% of tourists going to Las Vegas to gamble spend more than \$1,000. The Visitor’s Bureau of Las Vegas wants to update this percentage.

1. The new study is to use the 90% confidence level. The estimate is to be within 1% of the population proportion. What is the necessary sample size?
2. The Bureau feels the sample size determined above is too large. What can be done to reduce the sample? Based on your suggestion, recalculate the sample size.

End of chapter exercises:

Question 32:

The American Restaurant Association collected information on the number of meals eaten outside the home per week by young married couples. A survey of 60 couples showed the sample mean number of meals eaten outside the home was 2.76 meals per week, with a standard deviation of 0.75 meals per week. Construct a 99% confidence interval for the population mean.

Question 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 the result.

Question 52:

A random sample of 25 people employed by the Florida state authority established they earned an average wage (including benefits) of \$65.00 per hour. The sample standard deviation was \$6.25 per hour.

1. What is the population mean? What is the best estimate of the population mean?
2. Develop a 99% confidence interval for the population mean wage (including benefits) for these employees.
3. How large a sample is needed to assess the population mean with an allowable error of \$1.00 at 95% confidence?

Question 62:

The Tennessee Tourism Institute (TTI) plans to sample 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 a 95% confidence level the population proportion with an allowable error of 2%?

End of chapter Data Set Exercise (Show all calculations):

Question 64:

Refer to the Baseball 2010 data (attached to this order), which report information on the 30 Major League Baseball teams for the 2010 season.

1. Develop a 95% confidence interval for the mean number of home runs per team.
2. Develop a 95% confidence interval for the mean number of errors committed by each team.
3. Develop a 95% confidence interval for the mean number of stolen bases for each team.

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