# A manufacturer wants to increase the shelf life of a line of cake mixes.

1. Conduct a one-tailed hypothesis test given the information below. A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix had a mean of 217.222 and a standard deviation of 1.2019. At the 0.025 significance level, what is the critical value? State the null and alternative hypothesis. Draw a diagram. Provide the computation of the test statistic. State your decision in terms of the null hypothesis.

2. A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected and their times (in seconds) to access the website with the old and new designs were recorded. The results follow. Let α = 0.05. Is the mean time to access the new website design shorter, or is (time for the old design - time for the new design) greater than zero? Express your answer in terms of the null hypothesis.

3. Conduct a two-tailed hypothesis test given the information below. A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are presented next. A. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but assumed equal. What is the critical t value at the 1% level of significance? Note: The table in the exam is for one-tail tests—be sure to double the percentage for a two-tail test. B. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. If we test the null hypothesis at the 1% level of significance, what is the decision?

4.The production of car tires in any given year is related to the number of cars produced that year and in prior years. Suppose our econometric model resulted in the following data. Regression Coefficient t-Statistic p-Value X1 = Cars Produced This Year 5.00 10.4 0.0000 X2 = Cars Produced Last Year 0.25 0.6 0.5499 X3 = Cars Produced 2 Years Ago 0.67 1.4 0.1646 X4 = Cars Produced 3 Years Ago 2.12 2.7 0.0081 X5 = Cars Produced 4 Years Ago 3.44 6.5 0.0000 Constant -50,000 Multiple R 0.83 R Squared ? Why is the coefficient for “cars produced this year” a positive number? Which is the most statistically significant variable? What evidence shows this? Which is the least statistically significant variable? What evidence shows this? For a 0.05 level of significance, should any variable be dropped from this model? Why or why not? What is the R Squared Value? What is the interpretation?

7.Define autocorrelation in the following terms: a. In which type of regression is it likely to occur? b. What is the negative impact of autocorrelation in a regression? c. Which method is used to determine if it exists?

8.Define multicollinearity in the following terms: a. In which type of regression is it likely to occur? b. What is the negative impact of multicollinearity in a regression? c. Which method is used to determine if it exists? d. If multicollinearity is found in a regression, how is it eliminated? d. If found in a regression, how is autocorrelation eliminated?

2. A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected and their times (in seconds) to access the website with the old and new designs were recorded. The results follow. Let α = 0.05. Is the mean time to access the new website design shorter, or is (time for the old design - time for the new design) greater than zero? Express your answer in terms of the null hypothesis.

3. Conduct a two-tailed hypothesis test given the information below. A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are presented next. A. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but assumed equal. What is the critical t value at the 1% level of significance? Note: The table in the exam is for one-tail tests—be sure to double the percentage for a two-tail test. B. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. If we test the null hypothesis at the 1% level of significance, what is the decision?

4.The production of car tires in any given year is related to the number of cars produced that year and in prior years. Suppose our econometric model resulted in the following data. Regression Coefficient t-Statistic p-Value X1 = Cars Produced This Year 5.00 10.4 0.0000 X2 = Cars Produced Last Year 0.25 0.6 0.5499 X3 = Cars Produced 2 Years Ago 0.67 1.4 0.1646 X4 = Cars Produced 3 Years Ago 2.12 2.7 0.0081 X5 = Cars Produced 4 Years Ago 3.44 6.5 0.0000 Constant -50,000 Multiple R 0.83 R Squared ? Why is the coefficient for “cars produced this year” a positive number? Which is the most statistically significant variable? What evidence shows this? Which is the least statistically significant variable? What evidence shows this? For a 0.05 level of significance, should any variable be dropped from this model? Why or why not? What is the R Squared Value? What is the interpretation?

7.Define autocorrelation in the following terms: a. In which type of regression is it likely to occur? b. What is the negative impact of autocorrelation in a regression? c. Which method is used to determine if it exists?

8.Define multicollinearity in the following terms: a. In which type of regression is it likely to occur? b. What is the negative impact of multicollinearity in a regression? c. Which method is used to determine if it exists? d. If multicollinearity is found in a regression, how is it eliminated? d. If found in a regression, how is autocorrelation eliminated?

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