Question 1

DEPARTMENT OF ECONOMICS

SECOND SEMESTER 2015/2016 ACADEMIC YEAR

ECON214: Elements of Statistics for Economists (3 Credits)

Practice Questions 3

Question 1

The claims department of an insurance company reports that the mean cost to process a claim, handle all the paperwork, pay the investigator, and so on is $60. An industry comparison showed this amount was larger than most other insurance companies, so they instituted cost-cutting measures. To evaluate the effect of the cost-cutting measures, the company selected a random sample of 45 claims and found the mean of this sample was $57 and the standard deviation $10. At the 0.01 significance level should they conclude the cost-cutting measures actually reduced the cost? Or should they conclude that the difference of $3 between the sample mean ($57) and the population mean ($60) is due to chance?

Question 2

One of the largest firms making and marketing hip-life music in Ghana has changed its manager responsible for acquiring new musical talent. In the past, at least 35% of recording contracts have resulted in hits. The top management of the firm wishes to find out if the proportion has decreased with the new manager. They decide that they will collect data on how many of recording contracts made by the new manager have resulted in hits.

(a) State the appropriate null and alternative hypotheses.

(b) Choose a test statistic and rejection rule to test the null hypothesis at the 1% significance level, using a sample of 70 new contracts.

(c) The sample of 70 contracts resulted in 17 hits. Should the null hypothesis be rejected? Explain your answer.

(d) Would the decision about the null hypothesis be different at the 5% significance level? Explain your answer.

Question 3

A firm has two plants, each of which produces screws. It is necessary to test whether the mean diameter of the screws produced at one plant equals the mean diameter of those produced at the other plant. If the mean diameter of screws at either plant is larger than that at the other plant, the hypothesis that the mean diameters at the two plants are equal will have to be rejected. At both plants the standard deviation of the diameters of the screws is 0.01 inches. A random sample of 100 screws is taken from each plants output, and the sample mean is found to be 0.41 inches at the one plant and 0.45 inches at the other. If the significance level is 0.05, should the firm reject the hypothesis that the means are equal?

Question 4

A polling organization is interested in determining whether a candidate for parliamentary elections will run better in urban or in rural areas. A random sample is drawn of 400 urban voters and 400 rural voters, and it is determined that 55% of urban voters and 49% of rural voters prefer this candidate over others. Should the polling organization conclude that the popularity of this candidate differs between urban and rural areas? Use = 0.05.

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