# Statistics Project on Broyles Textbook Practice Exercise (Statistics Project Sample)

Complete Practice Exercise 11 (page 157) and Practice Exercise 11 (page 180) in the textbook. For the data set listed, use Excel to extract the mean and standard deviation for the sample of lengths of stay for cardiac patients. Use the following Excel steps:

Enter the data set into Excel.

Click on the Data tab at the top.

Highlight your data set with your mouse.

Click on the Data Analysis tab at the top right.

Click on Descriptive Statistics in the analysis tool list.

Find the mean and standard deviation of the data sets.

Exercises

156 Chapter 6: Inferences Concerning the MeanR,O

1. To estimate the time required to provide a given laboratory procedure, suppose that we measured

the amount of time required when the service was provided on 60 occasions. Based on this

sample, we obtained a mean of 20.32 minutes and a standard deviation of 3.82 minutes.What

can we say with a probability of 0.95 about the size of the error when we use 20.32 minutes as an

estimate of the true average time required to provide the procedure?

(Hint: – X Z/2 [S/√n])

2. Use the data in Exercise 1 to construct a 98% confidence interval.

3. Based on a sample of 90 patients, suppose that we found that the average cost of diagnosing and

treating an upper respiratory infection is $490 with a standard deviation of $50. Use these data

to construct a 95% confidence interval.What can be said with a probability of 0.99 about the possible

size of the error that results if we use $490 as an estimate of the true average cost of treating

an upper respiratory infection? (Hint: -X Z/2 [S/√n])

4. Our health organization is interested in estimating the average value of outstanding accounts receivable. After selecting a sample of 100 accounts, suppose that the mean was $120 and the standard deviation was $40. Use these data to construct a 98% confidence interval.

5. Suppose that we know that the average length of stay for 100 patients was 3.5 days and that the

standard deviation was 2.5 days. Construct a 95% confidence interval for the true mean length of

stay.

6. In a study of 10 patients treated for a kidney infection, the following data refer to the use of urinary analysis. 1, 2, 5, 7, 3, 1, 4, 3, 6, 4 Use these data to construct a 99% confidence interval for the true mean use of the procedure. 7. In a study of the cost per case of treating patients admitted with a disease of the digestive system, the following data were obtained:

$5,000, $5,500, $9,000, $8,000, $10,500, $11,000, $490

Use these data to construct a 98% confidence interval for the true mean cost per case.

8. Suppose that we selected 12 outstanding accounts and measured the time that was required to

convert each into cash after the first billing. The results in days are as follows:

120, 50, 40, 180, 230, 250, 30, 60, 70, 180, 270, 190

Use these data to construct a 98% confidence interval for the true mean time required to transform

accounts into cash after the first billing. 9. Suppose that the data in Exercise 8 were collected after the introduction of a new collection method. Before the use of the new method, the average time required to transform an account into cash was 230 days. If 0.05, determine whether the new

procedure was successful in reducing the collection period.

10. Suppose that a labor union claims that a given procedure requires 20 minutes to perform. To

evaluate this, suppose that we measured the amount of time required to complete the procedure

on each of 36 occasions. 12, 15, 18, 14, 19, 21, 16, 17, 18, 13, 19, 21, 22, 15, 16, 17, 18, 22

23, 14, 16, 18, 23, 13, 16, 18, 19, 15, 13, 21, 23, 14, 15, 16, 17, 21

Assuming we wish to be 95% certain of avoiding a Type I error, use these data to evaluate the

union's claim.

11. Suppose that a health plan asserts that a patient hospitalized with coronary heart disease requires no more than 6.5 days of hospital care. However, we believe that a stay of 6.5 days is too low. To examine the claim of the health plan, assume further that we collected data depicting the lengths of stay of 40 patients who were hospitalized recently with coronary heart disease. The results of the sample are as follows:

5, 8, 9, 12, 7, 9, 10, 11, 4, 7, 8, 5, 8, 13, 11, 10, 6, 5, 8, 9, 5, 12, 7, 9, 4, 8, 7, 7, 11, 5, 8, 10, 5,

8, 2, 11, 3, 6, 8, 7

If 0.05, use these data to evaluate the claim by the health plan.

12. Suppose that our multiinstitutional arrangement serves a well-defined population and operates two clinics that serve two separate market or service areas.We believe that distance

keeps people from seeking care and are concerned that, on average, the distance traveled from

the patient's residence to Clinic A exceeds that of Clinic B. To assess the existence of a potential problem, suppose that we surveyed 25 individuals in each market and obtained information describing the miles to the clinic

A: 4, 7, 10, 13, 21, 14, 1, 2, 6, 7, 1, 4, 2, 14, 18, 2, 3, 10, 2, 7, 11, 4, 6, 6, 3

B: 2, 4, 1, 6, 7, 10, 3, 2, 5, 9, 11, 13, 2, 1, 4, 6, 8, 8, 9, 3, 2, 5, 1, 6, 7

If we wish to be 95% certain of avoiding a Type I error, use these data to examine differences in the

average distance traveled to the two clinics.

13. Suppose that we wish to evaluate the performance of two technicians and measure the amount

of time each required to perform a given procedure on 20 different occasions. The results of the

two samples are as follows: Technician 1: 30, 31, 29, 32, 30, 29, 28, 27, 29, 30, 31, 29, 28, 30,

31, 30, 29, 29, 32, 31

Technician 2: 28, 29, 29, 32, 33, 28, 27, 28, 29, 30, 27, 30, 28, 29, 27, 27, 29, 30, 27, 28

http://www(dot)excel-easy(dot)com/examples/descriptive-statistics.html

BROYLES TEXTBOOK PRACTICE EXERCISE

Name

Institution

Date

Exercises156 Chapter 6: Inferences Concerning the MeanR,O1. To estimate the time required to provide a given laboratory procedure, suppose that we measured the amount of time required when the service was provided on 60 occasions. Based on this sample, we obtained a mean of 20.32 minutes and a standard deviation of 3.82 minutes. What can we say with a probability of 0.95 about the size of the error when we use 20.32 minutes as an estimate of the true average time required to provide the procedure?(Hint: – X Z /2 [S/√ n])

n= 60

Mean= 20.32

Standard deviation=3.82

Size of error

Probability 95%

X Z /2 [S/√ n]) = 20.32

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