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Chapter 6: Q10E (page 339)

Question: Heart rate variability of police officers. Are police officers susceptible to higher-than-normal heart rates? The heart rate variability (HRV) of police officers was the subject of research published in the American Journal of Human Biology (January 2014). HRV is defined as the variation in time intervals between heartbeats. A measure of HRV was obtained for each in a sample of 355 Buffalo, N.Y., police officers. (The lower the measure of HRV, the more susceptible the officer is to cardiovascular disease.) For the 73 officers diagnosed with hypertension, a 95% confidence interval for the mean HRV was (4.1, 124.5). For the 282 officers who are not hypertensive, a 95% confidence interval for the mean HRV was (148.0, 192.6).

a. What confidence coefficient was used to generate the confidence intervals?

b. Give a practical interpretation of both 95% confidence intervals. Use the phrase “95% confident” in your answer.

c. When you say you are “95% confident,” what do you mean?

d. If you want to reduce the width of each confidence interval, should you use a smaller or larger confidence coefficient? Explain.

Short Answer

Expert verified

Answer

  1. 95%
  2. 95% of the repeated samples taken will contain the population mean.
  3. 95% of the times, one can be successful
  4. No.

Step by step solution

01

Determining the confidence coefficient 

a.

The confidence coefficient is nothing but the exact level of confidence considered by the researcher. In this case, for conducting the test on the heart rate variability of 73 police officers is 95%.

02

Elucidation on practical interpretation

b. Suppose repeated samples are taken into consideration by the researchers in the research process, and the 95% confidence interval is computed for every sample separately. That time out of all the intervals, 95% of them would contain the population mean

03

Meaning of 95 percent confident 

When anybody says before attempting anything that he/she is 95% confident, it means that if the event occurs 100 times, then he/she can win 95 times. This is applicable in the research processes also by the researchers.

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Most popular questions from this chapter

Accounting and Machiavellianism. Refer to the Behavioral Research in Accounting(January 2008) study ofMachiavellian traits in accountants, Exercise 6.19 (p. 341),where a Mach rating score was determined for each ina sample of accounting alumni who work as purchasingmanagers. Suppose you want to reduce the width of the95% confidence interval for the true mean Mach ratingscore of all purchasing managers you obtained in Exercise 6.19b. How many purchasing managers should be includedin the sample if you desire a sampling error of only 1.5Mach rating points? Useσ≈12 in your calculations.

Question: Auditing sampling methods. Traditionally, auditors have relied to a great extent on sampling techniques, rather than 100% audits, to help them test and evaluate the financial records of a client firm. When sampling is used to obtain an estimate of the total dollar value of an account—the account balance—the examination is known as a substantive test (Audit Sampling—AICPA Audit Guide, 2015). In order to evaluate the reasonableness of a firm’s stated total value of its parts inventory, an auditor randomly samples 100 of the total of 500 parts in stock, prices each part, and reports the results shown in the table.

a. Give a point estimate of the mean value of the parts inventory.

b. Find the estimated standard error of the point estimate of part a.

c. Construct an approximate 95% confidence interval for the mean value of the parts inventory.

d. The firm reported a mean parts inventory value of $300. What does your confidence interval of part c suggest about the reasonableness of the firm’s reported figure?

Question:FindZα2foreachofthefollowing:a.α=.10b.α=.01c.α=.05d.α=.20

Question: Let t0 be a specific value of t. Use Table III in Appendix D to find t0 values such that the following statements are true.

a.P(t≥t0)=.025wheredf=11b.P(t≥t0)=.01wheredf=9c.P(t≤t0)=.005wheredf=6d.P(t≤t0)=.05wheredf=18

Splinting in mountain climbing accidents. The most common injury that occurs among mountain climbers is trauma to the lower extremity (leg). Consequently, rescuers must be proficient in immobilizing and splinting fractures. In High Altitude Medicine & Biology (Vol. 10, 2009), researchers examined the likelihood of mountain climbers needing certain types of splints. A Scottish Mountain Rescue study reported that there was 1 femoral shaft splint needed among 333 live casualties. The researchers will use this study to estimate the proportion of all mountain casualties that require a femoral shaft splint.

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b. Use Wilson’s adjustment to find a 95% confidence interval for the true proportion of all mountain casualties that require a femoral shaft splint. Interpret the result
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