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Chapter 7: Q 127 SE (page 443)

Question:Accounting and Machiavellianism. Refer to the Behavioral Research in Accounting (January 2008) study of Machiavellian traits in accountants, Exercise 6.19 (p. 341). A Mach rating score was determined for each in a random sample of 122 purchasing managers, with the following results:x̄ = 99.6 s = 12.6. Recall that a director of purchasing at a major firm claims that the true mean Mach rating score of all purchasing managers is 85.

a. Suppose you want to test the director’s claim. Specify the null and alternative hypotheses for the test.

b. Give the rejection region for the test using α = 0.10.

c. Find the value of the test statistic.

d. Use the result, part c, to make the appropriate conclusion.

Short Answer

Expert verified
  1. The null and alternative hypotheses are H0 : µ = 85against Ha : µ ≠ 85.
  2. Reject the null hypothesis if z < -1.64 or z > 1.64.
  3. The value of the test statistic is z = 12.7986.
  4. There is not enough evidence to support the director’s claim that all purchasing managers' true mean Mach rating score is 85.

Step by step solution

01

Given Information

  • The claim of the director of purchasing at a major firm is that the true Mach score of all purchasing managers is 85.
  • The significance level for the hypothesis testing problem is α = 0.10.
  • A Mach rating score for a random sample 122 purchasing managers is provided.
  • The summary statistics are:x̄ = 99.6 s = 12.6.
02

Setting the null and alternative hypothesis

(a)

The researchers are interested in the central value of the population, commonly known as the parameters. The claim about the population parameters is validated by using hypothesis testing.

The null and alternative hypotheses for the director’s claim are:

The null and alternative hypotheses are H0 : µ = 85against Ha : µ ≠ 85.

03

Obtaining the rejection region

(b)

The rejection region for the two-tailed test lies at both the tail of the test statistic distribution.

The z-critical value at a 10% level of significance for a two-tailed test is:

The critical values are obtained by using the z-table.

Therefore, reject the null hypothesis if z < -1.64 or z > 1.64.

04

Computing the test statistic

(c)

In a hypothesis testing problem, when a sufficiently large sample is drawn from a population z-test is used.

The test statistic is

The value of the test statistic is z = 12.7986.

05

Conclusion

(d)

Referring to part c., the test statistic is z = 12.7986. The rejection region is z < -1.65 or z > 1.65.

The value of the test statistic is checked; if it lies in the rejection region, the null hypothesis is rejected.

The test statistic 12.7986 lies in the rejection region; hence the null hypothesis is rejected.

Therefore, there is not enough evidence to support the director’s claim that all purchasing managers' true mean Mach rating score is 85.

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