(a) Calculate and interpret the covariance between x and y. (3%)

a. At α = 0.1, does the data provide sufficient evidence to indicate that the standard deviations of two populations are different? (6%)

b. At α = 0.1, does the data provide sufficient evidence to indicate that the mean of population 1 is larger than the mean of population 2? (6%)

2. A journal surveyed its readers and asked how each rated the quality of management and the reputation of the company for over 250 worldwide corporations. Both the quality of management and the reputation of the company were rated on an excellent, good and fair categorical scale. Assume the sample data for 200 respondents below applies to this study. Use a 0.05 level of significance and test for independence of the quality of management and the reputation of the company. (8%)

a. Construct an analysis of variance table to test whether there is a significant difference among the means of three treatments. (6%)

b. Use Fisher’s LSD approach to determine which populations have different means.,where Si  is the sample standard deviation of treatment i, i =1, 2, 3. (6%)

a. Find the best-fitting line for the above data. (6%)

b. According to the information above, at a 0.05 level of significance, test for the claim “longer the years of experience, more the annual sales.”. (6%)

c. If the number of years of experience is 10 years, find the 95% confidence interval for the corresponding mean annual sales. (6%)

(b) Calculate the coefficient of correlation, and comment on the relationship between x and y. (3%)

(c) Determine the least squares line, and use it to estimate the value of y for x = 6. (3%)

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