# ISU STAT 226 - FinalReviewSpring2017 (10 pages)

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## FinalReviewSpring2017

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- School:
- Iowa State University
- Course:
- Stat 226 - Intr Busines Stat I

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Introduction to Business Statistics I Final Exam Review May 2nd 2017 Review Instructor Michael S Czahor Statistics Department Intro to Business Statistics I 1 Kangaroo Example 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 Statistics Department Intro to Business Statistics I During 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 2 Question 1 Identify the two types of graphical displays surrounded by the red box Kangaroo Example Question 2 Identify the shape of the distributions for both variables of interest Output from Kangaroo Data Statistics Department Intro to Business Statistics I 3 Kangaroo Example Question 3 Question 6 Question 9 What is the correlation between male grey kangaroo nasal lengths and nasal widths for the randomly sampled kangaroos Write out the model for the fitted least squares regression line produced in JMP a Predict the nasal width in mm of a male grey kangaroo if their nasal length is 0 65 meters Question 4 Question 7 Describe the scatterplot using the four key features discussed in class Note The correlation describes two of these four features Interpret the slope and intercept see red box within the context of the problem b Suppose a kangaroo has a nasal length of 620 mm and a nasal width of 233 mm Calculate their residual Question 5 Question 8 Question 10 Based on the scatterplot and fitted line Identify the explanatory and response variable Construct a 90 confidence interval for the population slope see red box for output Statistics Department Intro to Business Statistics I Is the prediction from Question 9 valid Explain 4 Question 11 State the four necessary assumptions that are needed for regression inference Do the assumptions hold in our example Link the assumptions to the correct plots Kangaroo Example Question 12 Test 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 13 I 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 level Question 14 Suppose 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 Statistics Department Intro to Business Statistics I 5 Question 15 Using the information from Question 14 what is the probability that a male grey kangaroo has a nasal width larger than 240 mm Kangaroo Example Question 16 Using 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 17 The nasal width that marks the 63rd percentile from the distribution in Question 16 is Question 18 Suppose 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 19 The margin of error in Question 18 is and would increase decrease if the confidence level increased Question 20 Question 21 A 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 What is the five number summary for the nasal widths of the forty five randomly selected male grey kangaroos Statistics Department Intro to Business Statistics I 6 Overall Review Part 1 Statistics Department Intro to Business Statistics I 7 Overall Review Part 2 Statistics Department Intro to Business Statistics I 8 Overall Review Part 3 8 Statistics Department Intro to Business Statistics I 9 Overall Review Part 4 Statistics Department Intro to Business Statistics I 10

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