Time Series

Question

1. What are the components of a time series? What external factors might affect each of the different components? 

2. What is the purpose of forecasting? Why are forecasts not always correct? What are the limitations of forecasting? 

3. Why is the trend commonly thought to be the most important component of forecasting? How is the linear trend method related to linear regression? Why are simple moving averages and weighted averages commonly used forms of forecasting? 

4. What is an index number as relates to time series analysis? In a regression of a time series that states data as a function of calendar year, what requirement of regression is violated? How might one overcome this requirement and still perform a successful time series analysis?

Question

The manufacturer of the ColorSmart-5000 television set claims that 95 percent of its sets last at least five years without needing a single repair. In order to test this claim, a consumer group randomly selects 400 consumers who have owned a ColorSmart-5000 television set for five years. Of these 400 consumers, 316 say that their ColorSmart-5000 television sets did not need repair, while 84 say that their ColorSmart-5000 television sets did need at least one repair.

a.: Letting p be the proportion of ColorSmart-5000 television sets that last five years without a single repair, set up the null and alternative hypotheses that the consumer group should use to attempt to show that the manufacturer’s claim is false.

b.: Use critical values and the previously given sample information to test the hypotheses you set up in part α by setting α equal to .10, .05, .01, and .001. How much evidence is there that the manufacturer’s claim is false?

c.: Do you think the results of the consumer group’s survey have practical importance? Explain your opinion.