Business Statistics Questions

Answer the following five (5) questions. Show all work. Ten (10) points each. Partial credit may be awarded. Suppose we have the following information from a simple regression: b_0=117.4,b_1=-14.39,s_(b_0 )=44.17,s_(b_1 )=3.20,n=300,x ̅=4.3,SST=17045,and SSE=12053. What is the coefficient of determination? What is the correlation coefficient? What is the sample mean of Y? Test the hypothesis H_0:β_1=0 vs. H_1:β_1≠0, with α = 0.05. The Daytona Beach Tourism Commission is interested in the average amount of money a typical college student spends per day during spring break. It is presumed that daily spending habits are normally distributed. They survey 35 students and find that the mean daily spending is $63.57 with a sample standard deviation of $17.32. Develop a 95% confidence interval for the population mean daily spending. What level of confidence is associated with an interval of $58.62 to $68.52 for the population mean daily spending? The sales manager for a hardware wholesaler finds that 229 of the previous 500 calls to hardware store owners resulted in new product placements. Assume these 500 calls represent a random sample. Develop a 95% confidence interval for the population proportion of new product placements. What level of confidence is associated with an interval of .400513 to .515487 for the population proportion of new product placements? A pharmaceutical manufacturer is concerned that the mean impurity concentration in pills should not exceed 2%. It is known that impurity concentrations follow a normal distribution with a population standard deviation 0.32%. A random sample of 64 pills from a production run was checked, and the sample mean impurity concentration was found to be 2.05%. Test at the 5% level the null hypothesis that the population mean impurity concentration is 2% or less against the alternative that it is more than 2%. Calculate the p-value for this test. It is hypothesized that the number of bottles of an imported premium beer sold in city restaurants depends linearly on the average cost of meals in these restaurants. The following results were obtained for a sample of n = 20 restaurants of approximately equal size: x ̅=30,y ̅=18.8,Var(x)=412,Cov(x,y)=212 where: y = Number of bottles of imported premium beer sold, and x = Average cost, in dollars, of a meal. Determine the equation for the sample regression line. Interpret the slope of the sample regression line. Is it possible to provide a meaningful interpretation of the intercept of the sample regression line? Explain.