MGT 5028 Week 5 Assignment -Application Questions and Problems

Introduction:Correlation, Causation, and PredictionStatistical calculations focus on analyzing and interpreting scatterplots, creating a scatterplot using statistical software, performing simple regression and correlational analyses, and inferring population characteristics from samples. The world is, to say the least, a complicated place. By using statistics that show us how elements in it are related, we may simplify the manageability of the world and perhaps even be able to predict some future outcomes. In this assignment, you will be helped to understand the relationship of correlation causation and prediction.****************************************Week 5 Assignment: Complete Application Questions and ProblemsActivity DescriptionDownload Data File 4 and complete the problems and questions as presented. Show your work (either your hand calculations or your statistical program output). You may either scan your handwritten work and submit it as a low-resolution graphic, type your answers directly into the document, or cut and paste your work into a Word file. Be sure to name the file using the proper NCU naming conventions before its submittal.Data File 4Show all your workChapter SevenProblem 1) Look at the scatterplot below. Does it demonstrate a positive or negative correlation? Why?Are there any outliers? What are they?Problem 2) Look at the scatterplot below. Does it demonstrate a positive or negative correlation? Why?Are there any outliers? What are they?Problem 3) The following data come from your book, problem 26 on page 247. Here is the data:Mean daily caloriesInfant Mortality Rate (per 1,000 births)152315434956194111426782416101073443616401533362734294426717a) For the above data construct a scatterplot using SPSS or Excel (Follow instructions onpage 244 of your textbook). What does the scatterplot show? Can you determine a typeof relationship? Are there any outliers that you can see?b) Using the same data conduct a correlation analysis using SPSS or Excel. What is thecorrelation coefficient? Is it a strong, moderate or weak correlation? Is the correlationsignificant or not? If it is what does that mean?Problem 4)Bill is doing a project for you in the marketing department. In conducting his analysis regardingconsumer behavior and a new product that has come out, he tells you the correlation between thesetwo variables is 1.09. What is your response to this analysis?Problem 5)Judy has conducted an analysis for her supervisor. The result she obtained was a correlationcoefficient that was negative 0.86. Judy is confused by this number and feels that because it isnegative and not positive, is means that it is bad. You are her supervisor. How would you clarifythis result for Judy regarding the meaning of the correlation?Problem 6)Explain the statement, correlation does not imply causality.Problem 7)Using the best-fit line below for prediction, answer the following questions:a) What would you predict the price of Product X in volume of 150 to be (approximately)?b) What would you predict the price of Product X in volume of 100 to be (approximately)?Problem 8)You are interested in finding out if a students ACT score is a good predictor of his or her final collegegrade point average (GPA). You have obtained the following data and are going to conduct a regressionanalysis with these figures:ACTGPA22.03.032.03.7833.03.6821.02.9427.03.3825.03.2130.03.65a) What is the R? What type of relationship does it indicate (strong/weak; positive/negative)?b) Go to the coefficients readout. The constant is the intercept. Under that is the ACT and that is theslope. Using the straight line formula of Y = mx + b, which you will find on page 262, you will nowpredict some future GPA scores: In the formula (m) is the slope; (x) is the variable that you are lookingto use as a predictor; and (b) is the intercept. Predict GPA from the following ACT scores using theregression equation/straight line formula (show all your work):1) 202) 253) 34Chapter EightShow all your workProblem 1)A sample of nine students is selected from among the students taking a particular exam. The nine studentswere asked how much time they had spent studying for the exam and the responses (in hours) were asfollows:18, 7, 10, 13 12, 16, 5, 20, 21Estimate the mean study time of all students taking the exam. Round your answer to the nearest tenth of anhour, if necessary.Problem 2)Scores on a particular test have a mean of 64.6. The distribution of sample means for samples of size 100 isnormal with a mean of 64.6 and a standard deviation of 1.9. Suppose you take a sample of size 100 of testscores and find that the mean is 63. What is the z-score corresponding to this sample mean?Problem 3)There are 349 teachers at a college. Among a sample of 110 teachers from this college, 66 have doctorates.Based on this sample, estimate the number of teachers at this college without doctorates.Problem 4)Sample size = 400; sample mean = 44; sample standard deviation = 16. What is the margin of error?Problem 5)A sample of 64 statistics students at a small college had a mean mathematics ACT score of 28 with astandard deviation of 4. Estimate the mean mathematics ACT score for all statistics students at this college.Give the 95% confidence interval.Problem 6)A government survey conducted to estimate the mean price of houses in a metropolitan area is designed tohave a margin of error of $10,000. Pilot studies suggest that the population standard deviation is $70,000.Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.Problem 7)A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 490college students showed that 33% of them had, or intended to, cheat on examinations. Find the margin oferror for the 95% confidence interval.