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Chapter 6: Q1E (page 338)

FindZα/2for each of the following:

a.= .10

b.= .01

c.= .05

d.= .20

Short Answer

Expert verified
  1. 1.645
  2. 2.576
  3. 1.960
  4. 1.28

Step by step solution

01

ComputingZα/2  when α is 0.10

  1. Whenis 0.10, it means that α2will be equal to 0.05. From the z score table containing the level of significances,the associated critical value of z can be found to be 1.645.
02

Computing Zα/2 when α is 0.01

b. Whenis 0.01, it means that α2will be equal to 0.005. From the z score table containing the level of significances,the associated critical value of z can be found to be 2.576.

03

Computing Zα/2 when α is 0.05

c. Whenis 0.05, it means that α2will be equal to 0.025. From the z score table containing the level of significances, the associated critical value of z can be found to be 1.960

04

Computing Zα/2 when α is 0.20

d. Whenis 0.20, it means that α2will be equal to 0.10. From the z score table containing the level of significances, the associated critical value of z can be found to be 1.28.

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Most popular questions from this chapter

Question: A random sample of n measurements was selected from a population with unknown meanμand known standard deviationσ2. Calculate a 95% confidence interval forαfor each of the following situations:

a. n = 75, X = 28,σ2= 12

b. n = 200, X= 102, σ2= 22

c. n = 100, X= 15,σ2=.3

d. n = 100, X= 4.05, σ2= .83

e. Is the assumption that the underlying population of measurements is normally distributed necessary to ensure the validity of the confidence intervals in parts a–d? Explain.

Question: The mean and standard deviation of a random sample of n measurements are equal to 33.9 and 3.3, respectively.

a. Find a 95% confidence interval for μif n = 100.

b. Find a 95% confidence interval forμ if n = 400.

c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?

Lobster trap placement. Refer to the Bulletin of MarineScience(April 2010) study of lobster trap placement,Exercise 6.29 (p. 348). Recall that you used a 95% confidenceinterval to estimate the mean trap spacing (in meters)for the population of red spiny lobster fishermen fishing inBaja California Sur, Mexico. How many teams of fishermenwould need to be sampled in order to reduce the width ofthe confidence interval to 5 meters? Use the sample standarddeviation from Exercise 6.29 in your calculation.

Findχα22  and  χ1-α22from Table IV, Appendix D, for each of the following:

a. n = 10, = .05

b. n = 20, = .05

c. n = 50, = .01

Unethical corporate conduct. How complicit are entrylevel accountants in carrying out an unethical request from their superiors? This was the question of interest in a study published in the journal Behavioral Research in Accounting (July 2015). A sample of 86 accounting graduate students participated in the study. After asking the subjects to perform what is clearly an unethical task (e.g., to bribe a customer), the researchers measured each subject’s intention to comply with the unethical request score. Scores ranged from -1.5 (intention to resist the unethical request) to 2.5 (intention to comply with the unethical request). Summary statistics on the 86 scores follow: x¯=2.42,s=2.84.

a. Estimate μ, the mean intention to comply score for the population of all entry-level accountants, using a 90% confidence interval.

b. Give a practical interpretation of the interval, part a.

c. Refer to part a. What proportion of all similarly constructed confidence intervals (in repeated sampling) will contain the true value of μ?

d. Compute the interval, x¯±2s. How does the interpretation of this interval differ from that of the confidence interval, part a?

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