Introduction to Business Statistics IFinal Exam ReviewMay 2nd, 2017Review InstructorMichael S. CzahorStatistics DepartmentIntro to Business Statistics I1Kangaroo ExampleStatistics DepartmentIntro to Business Statistics I2During tonight’s review let’s assume that I have a random sample of 45 male grey kangaroos from ALL male grey kangaroos in the world.Assumptions: We will assume from previous knowledge that the population distributions for both nasal length (mm) and nasal width (mm) of all grey kangaroos are bell-shaped.An observational study was conducted to see if there is a relationship between the nasal length and nasal width of male grey kangaroos. A random sample of male grey kangaroos were measured and their nasal length and width was recorded in millimeters in the given data set analyzed in JMP.Kangaroo ExampleStatistics DepartmentIntro to Business Statistics I3Question 1Identify the two types of graphical displays surrounded by the red box.Question 2Identify the shape of the distributions for both variables of interest.Output from Kangaroo DataKangaroo ExampleStatistics DepartmentIntro to Business Statistics I4Question 3What is the correlation between male grey kangaroo nasal lengths and nasal widths for the randomly sampled kangaroos?Question 4Describe the scatterplot using the four key features discussed in class. Note: The correlation describes two of these four features.Question 5Based on the scatterplot and fitted line: Identify the explanatory and response variable.Question 6Write out the model for the fitted least squares regression line produced in JMP.Question 7Interpret the slope and intercept (see red box) within the context of the problemQuestion 8Construct a 90% confidence interval for the population slope !"(see$red$box$for$output).Question 9a) Predict the nasal width (in mm) of a male grey kangaroo, if their nasal length is 0.65 meters.b) Suppose a kangaroo has a nasal length of 620 mm and a nasal width of 233 mm. Calculate their residual.Question 10Is the prediction from Question 9 valid? Explain.Kangaroo ExampleStatistics DepartmentIntro to Business Statistics I5Question 11State the four necessary assumptions that are needed for regression inference. Do the assumptions hold in our example? Link the assumptions to the correct plots.Question 12Test if there exists a significant linear relationship between nasal length and nasal width for male grey kangaroos at the .10 significance level. Hint: State your hypothesis, calculate a test statistic, find a p-value, make a decision, and conclude with context.Question 13I now want to test if there is a positive linear relationship. Discuss the changes in: the hypotheses, test statistic, p-value, and decision/conclusion at the .10 significance levelQuestion 14Suppose the population mean of nasal widths for male grey kangaroos is 238 mm. From previous studies we know that the population standard deviation is 30 mm. What does the sampling distribution of the sample mean look like when the sample size is forty five? Note: You shouldn’t need the JMP output to answer this question.Kangaroo ExampleStatistics DepartmentIntro to Business Statistics I6Question 15Using the information from Question 14, what is the probability that a male grey kangaroo has a nasal width larger than 240 mm?Question 16Using the information from Question 14, what is the probability that the mean nasal width for 45 male grey kangaroos is greater than 240 mm?Question 17The nasal width that marks the 63rdpercentile from the distribution in Question 16 is ________.Question 18Suppose now that the population standard deviation is unknown. Using the output create an 80% confidence interval for the average nasal width of male grey kangaroos.Question 19The margin of error in Question 18 is ______ and would increase/decrease if the confidence level increased.Question 20A zoologist believes that the average nasal width of all male grey kangaroos is larger than 238 mm. Conduct a full hypothesis test to test the zoologist’s claim at the 0.05 significance level.Question 21What is the five number summary for the nasal widths of the forty five randomly selected male grey kangaroos?Statistics DepartmentIntro to Business Statistics I7Overall ReviewPart 1Statistics DepartmentIntro to Business Statistics I8Overall ReviewPart 2Statistics DepartmentIntro to Business Statistics I98Overall ReviewPart 3Statistics DepartmentIntro to Business Statistics I10Overall ReviewPart