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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:虫虅 = 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鈥檚 claim. Specify the null and alternative hypotheses for the test.

b. Give the rejection region for the test using 伪 = 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 : 碌 = 85against Ha : 碌 鈮� 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鈥檚 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 伪 = 0.10.
  • A Mach rating score for a random sample 122 purchasing managers is provided.
  • The summary statistics are:虫虅 = 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鈥檚 claim are:

The null and alternative hypotheses are H0 : 碌 = 85against Ha : 碌 鈮� 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鈥檚 claim that all purchasing managers' true mean Mach rating score is 85.

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Most popular questions from this chapter

Question: Point spreads of NFL games. Refer to the Chance (Fall 1998) study of point-spread errors in NFL games, Exercise 7.41 (p. 411). Recall that the difference between the actual game outcome and the point spread established by odds makers鈥攖he point-spread error鈥攚as calculated for 240 NFL games. The results are summarized as follows: . Suppose the researcher wants to know whether the true standard deviation of the point spread errors exceeds 15. Conduct the analysis using 伪 = 0.10.

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a. Specify the null and alternative hypotheses for this test.

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50 910 180 580 7800 4000 390 12100 3400 1300 11900 110

Suppose a random sample of 100 observations from a binomial population gives a value of \(\hat p = .63\) and you wish to test the null hypothesis that the population parameter p is equal to .70 against the alternative hypothesis that p is less than .70.

a. Noting that\(\hat p = .63\) what does your intuition tell you? Does the value of \(\hat p\) appear to contradict the null hypothesis?

If a hypothesis test were conducted using 伪= 0.05, for which of the following p-values would the null hypothesis be rejected?

a. .06

b. .10

c. .01

d. .001

e. .251

f. .042
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