STAT 2607 Assignment # 2 Winter 2016 Section A and B due Monday, February 22 before 3:00 PM Section C due Wednesday, February 24 before 1:05 PM INSTRUCTIONS: I. No late assignments will be accepted without su cient advanced notice and a legitimate, documented reason. Sec A and B: Assignments are to be uploaded to the course website on CULEARN as a single legible pdf le by the above due date and time. Sect C: Assignments are to be submitted in-class on the due date and prior to the beginning of the lecture. II. You must show all of your work. No credit will be given for answers without justication. No credit will be given for illegible work. III. Do not use MINITAB for any part of a question unless it specically says to do so. For questions that require MINITAB, you must include all relevant output with your assignment. The lab for this assignment will take place during the week of Feb 8, 2016. IV. This assignment is intended to represent your individual knowledge. It is not a group assignment. V. Data set les Demand.mtw and Doc and pop.mtw can be found on cuLearn. PART A: MINITAB QUESTIONS Question 1. The weekly demand for a product is believed to be normally distributed. Use the following procedure and data(Demand.mtw) to test this assumption. 18 20 22 27 22 25 22 27 25 24 26 23 20 24 26 27 25 19 21 25 26 25 31 29 25 25 28 26 28 24 (a) Use MINITAB to nd the mean, x , and standard deviation, s, of this data set. 1 1) Click Demand.mtw to open the data set. 2) Click Stat Basic Statistics Display Descriptive Statistics 3) When the Display Descriptive Statistics dialog box appears: Enter x in the Variables box Click OK (b) Divide the number line into 6 equal-probability intervals: p8, x z1 sq, rx z1 s, x z2 sq, rx z2 s, xq, rx, x ` z2 sq, rx ` z2 s, x ` z1 sq, rx ` z1 s, 8q First, use z table to nd z1 and z2 such that P pZ z1 q \" 1{6 and P pZ z2 q \" 2{6(Note that these are GREATER THAN probabilities). Then, use the x , s from (a) and z1 , z2 to compute these 6 intervals. (c) Assuming that the weekly demand for a product is normally distributed, the probability that a randomly selected week's demand will fall within each of these 6 intervals is 1{6. Compute the expected frequency under the normality assumption for each interval. Based on these expected frequencies, is it appropriate to conduct a chi-square goodness-of-t test? Why or why not? (d) Use the resultes from (c) and MINITAB to count the number of observed values that fall within each of these 6 intervals . For example, if you wish to nd the number of observations that fall within the interval [24.5, 25.8), enable the editor ( Click Editor Enable Commands ) and use the following command: MTB let c2 = (c1 \" 24.5 and c1 25.8) The column C2 will now contain a 1 for each demand that falls within the interval and a 0 for each demand that falls outside the interval. To nd the total number of observations that fall within the interval (i.e. the total number of 1s in column C2), use the following command: MTB tally c2 Do this for all six intervals to obtain the six observed frequencies. (e) Use the results from (c) and (d) to conduct a chi-square normality test for this data set. Use \" 0.05. Question 2. Refer to data set Doc and pop.mtw. The number of active physicians in a county(Y) is expected to be related to the total population of the county. Assume rst-order regression model is appropriate. (a) Develop a scatter plot with population as the independent variable(X). What does the scatter plot indicate about the relationship between the two variables? 2 1) Click Doc and pop.mtw to open the data set. 2) Click Graph Scatterplot 3) When the Scatterplots dialog box appears: Click Simple Click OK 4) When the Scatterplot: Simple dialog box appears: Enter NUM as Y Variable Enter POP as X Variable (b) Compute the least squares estimates of 0 and 1, and state the estimated prediction equation . 1) Click Stat Regression Regression Fit Regression Model 2) When the Regression dialog box appears: Enter NUM in the Response box Enter POP in the Predictors box Click OK (c) Plot the estimated prediction equation and the data. Use the same axes on which you graphed the scatter plot. Does the estimated prediction equation appear to t the data well? 1) Click Stat Regression Fitted Line Plot 2) When the Fitted Line Plot dialog box appears: Enter NUM in the Response box Enter POP in the Predictors box Click OK (d) What is the value of the sample correlation coe cient r? MINITAB Instructions for sub-question e). 1) Click Stat Basic Statistics Correlation 2) When the Correlation dialog box appears: Enter NUM POP in the Variables box Click OK PART B: WRITTEN QUESTIONS Question 3. The cost of a previously owned car depends upon factors such as make and model, model year, mileage, condition, and whether the car is purchased from a dealer or from a private seller. To investigate the relationship between the cars mileage and the sales price, data were collected on the mileage(X) and the sale price(Y) for 10 private sales of model year 2000 Honda Accords. Assume that a simple linear regression model is appropriate. 3 Miles(X) (1000s) Price(Y)($1000s) 90 7.0 59 7.5 66 6.6 87 7.2 90 7.0 106 5.4 94 6.4 57 7.0 138 5.1 87 7.2 The following is the summary statistics you may need for calculation: n \" 10, n i\"1 n i\"1 n i\"1 xi \" 874, n x2 \" 81540, i i\"1 n i\"1 yi \" 66.4 2 yi \" 446.62 xi yi \" 5667.7 (a) Compute b1 , b0 and the equation of the estimated regression line. (b) What is the estimate of expected change in price when mileage is increased by 1000 miles? (c) Compute SSE, s2 and s. (d) Compute the sample covariance sxy . (e) Compute and interpret the sample correlation coe cient r. Question 4. In a previous TV channels rating period, the percentages of viewers watching several channels in a certain time period in a major TV market were as follows: Station 1 Station 2 Station 3 Station 4 Others 15% 19% 22% 16% 28% In the current rating period, a survey of 2000 viewers gives the following frequencies: Station 1 Station 2 Station 3 Station 4 Others 281 410 567 282 460 1) Show that it is appropriate to carry out a chi-square goodness-of-t test for this data set. 2) Test to determine whether the viewing shares in the current rating period dier from those in the last rating period at the 10% level of signicance. If the result of the test is statistically signicant, describe the nature of the dierences using the two comparisons that contributed the greatest to the test statistic. 4 Question 5. A study of education levels of voters and their political party a liations yield the following results: Party A liation Education Level Liberal Conservative NDP Did not complete high school 40 20 10 High school degree 30 35 15 College degree 30 45 25 Use \" 0.01 to determine whether party a liation is independent of the educational level of voters. If you rejected the null hypothesis, describe the nature of the dierences using the three comparisons of observed and expected frequencies that contributed the greatest to the test statistic. Comment on the validity of your test results. 5