Statistics - Hypothesis Testing Projects

PROBLEM 1 : 9.13 Consider Exercise 9.12, and suppose that Consolidated Power has been experiencing technical

PROBLEM 1 :

9.13

Consider Exercise 9.12, and suppose that Consolidated Power has been experiencing technical problems with the cooling system. Because the system has been unreliable, the company feels it must take precautions to avoid failing to shut down the plant when its waste water is to warm. Other things being equal, should Consolidated Power set the probability of a Type 1 error equal to = .01 or - .05? Explain

"Exercise 12: Consolidated Power, a large electic power utility, has just build a modern nuclear power plant. This plant discharges waste water that is allowed to flow into the Atlantic Ocean. The Environment Protection Agency (EPA) has ordered that the waste water may not be excessively warm so that thermal pollution of the marine environment near the plant can be avoided. Because of this order, the waste water is allowed to cool in specially constructed ponds and is then released into the ocean. This cooling system works properly if the mean temperature of waste water discharged is 60 degrees F or cooler. Consolidated Power is required to monitor the temperature of the waste water. A sample of 100 temperature readings will be obtained each day, and if the sample results cast a substantial amount of doubt on the hypothesis that the cooling system is working properly (the mean temperature of waste water discharged is 60 degrees F or cooler), then the plant must be shut down and appropriate actions must be taken to correct the problem."

PROBLEM 2:

9.22

In Exercises 9.22 we consider using a random sample of 100 measurements to test H0: μ = 80 versus Ha: μ > 80. If $\bar{X}$ = 85 and $\sigma $ = 20:

How much evidence is there that H0: μ = 80 is false and H: μ > 80 is true?

PROBLEM 3:

12.10

A wholesaler has recently developed a computerized sales invoicing system. Prior to implementing this system, a manual system was used. The distribution of the number of

errors per invoice for the manual system is as follows:

Errors per Invoice 0 1 2 3 More Than 3

Percentage of Invoices 87% 8% 3% 1% 1%

After implementation of the computerized system, a random sample of 500 invoices gives the following error distribution:

Errors per Invoice 0 1 2 3 More Than 3

Number of Invoices 479 10 8 2 1

Show that it is appropriate to carry out a chi-square test using these data.
Use the following Excel output to determine whether the error percentages for the computerized system differ from those for the manual system at the .05 level of significance. What do you conclude?

pi Ei fi (f-E)^2/E

0.87 435 479 4.4506

0.08 40 10 22.5000

0.03 15 8 3.2667

0.01 5 2 1.8000

0.01 5 1 3.2000

Chi- 35.21724 p-value 0.0000001096

Square

PROBLEM 4 :

12.18a

In recent years major efforts have been made to standardize accounting practices in different countries; this is called harmonization. In an article in Accounting and Business Research, Emmanuel N. Emenyonu and Sidney J. Gray (1992) studied the extent to which accounting practices in France, Germany, and the United Kingdom are harmonized.

Depreciation method is one of the accounting practices studied by Emenyonu and Gray. Three methods were considered—the straight-line method (S), the declining balance method (D), and a combination of D & S (sometimes European firms start with the declining balance method and then switch over to the straight-line method when the figure derived from straight line exceeds that from declining balance). The data in Table 12.5 summarize the depreciation methods used by a sample of 78 French, German, and U.K. firms. Use these data and the MegaStat output to test the hypothesis that depreciation method is independent of a firm’s location (country) at the .05 level of significance.
T A B L E 1 2 . 5 Depreciation Methods Used by a Sample of 78 Firms
Depreciation Methods France Germany UK Total
1. Straight line (S) 15 0 25 40
2. Declining Bal (B) 1 1 1 3