4/6/2016 Stats 250 W16 HW 8 Closing date: 4/07/16 5:00PM 57050c98786f4a0b00d4d16a Question 1 Background : Good Cholesterol (HDL) Good Cholesterol (HDL) - A medical researcher in Calgary is interested in comparing the average HDL levels of cholesterol for male adults in Alberta, Canada, across four age groups, Group 1 = 20 to less than 30 years old, Group 2 = 30 to less than 40 years old, Group 3 = 40 to less than 50 years old, and Group 4 = 50 to less than 60 years old. Thus the researcher is interested in learning about the four population mean HDL levels i where i = 1, 2, 3, and 4 for the four respective age groups. A sample of 25 adult males from each age category is selected from the medical registry that is maintained in Calgary. The most recent HDL level for each selected adult male was recorded. Question 1 Subquestions 1.a 0.5 point(s) The initial ANOVA will assess if the population mean HDL levels are the same, namely, H0: 1 = 2 = 3 = 4. Which of the following is the correct and complete alternative hypothesis, Ha. The population mean HDL levels are all different. At least one mean is different. At least one population mean HDL level is different. 1 2 3 4 1.b 1 point(s) True/False: Each of the four samples of 25 adult males needs to be considered a random sample, representative of the corresponding four populations, so the results from these samples can be used to infer to these four populations. True False 1.c 1 point(s) 1/9 4/6/2016 True/False: An assumption that is needed for the ANOVA results to be valid is that the samples of HDL levels have the same variance. True False 1.d 0 point(s) Which of the following are appropriate ways to use your data to assess the 'equal variance' assumption that is needed for ANOVA? Select all that are appropriate. Check that the four sample standard deviations for HDL levels are similar; that is, the largest standard deviation is not more than twice the smallest standard deviation. Examine side-by-side boxplots for the four samples of HDL levels and assess if the IQRs (length of the boxes) and the overall ranges are similar. Use R to conduct Levene's test and check that the resulting p-value is small enough, less than 0.10. 1.e 0 point(s) In examining the data graphically, there was one very low outlier in Group 1 (20 to less than 30 year olds). It was found that this level was not even a possible HDL level, but no replacement level was available. Thus this one value was removed from Group 1 for a sample size of 24 for this age group. What of the following distributions would be used to find the p-value for the ANOVA hypothesis H0: 1 = 2 = 3 = 4? N(0,1) distribution t(3) distribution F(3,95) distribution F(3,99) distribution Question 2 Background : Prosthodontics Prosthodentists specialize in the use of dental implants, dentures, and crowns. Repairing chipped veneer is less time consuming than complete restoration, so a researcher wants to compare four different repair kits (1 = Cojet, 2 = Silistor, 3 = Cimara, and 4 = Ceramix) with respect to the average bond strength. The researcher randomly divided 20 equivalent porcelain veneer specimens into four treatment groups and chipped each specimen (in the 2/9 4/6/2016 same way) so each chip could be repaired with one of the four different repair kits. Each chip repair was evaluated for bond strength (units = MPa, megapascals). Three of the specimens were damaged resulting in the following data. Question 2 Subquestions 2.a 0.5 point(s) A partially completed ANOVA table is provided below. Report the missing values that should be in cells (A) to (F). Show your work, rounding values to two decimal places if rounding is necessary. Student answer No answer entered. 2.b 1 point(s) We vaguely remember that an assumption about normality is required to perform the inference. What is this assumption? The bond strengths for the sample of 17 repaired chips should be normally distributed. The bond strengths for the population of all such repaired chips should be normally distributed. The bond strengths for each of the four samples of repaired chips each should be normally distributed. The bond strengths for each of the four populations of all such repaired chips should be normally distributed. 2.c 1 point(s) To assess the normality condition, how many QQ plots should be examined? None, since we have a large enough sample size 3/9 4/6/2016 1 QQ plot for all 17 bond strengths 4 QQ plots, one for each sample of bond strengths for the 4 different repair kits 2.d 0 point(s) Complete the following statement in reference to this incorrect null hypothesis, H0: x 1 = x 2 = x 3 = x 4 . \"No, no! Hypotheses are supposed to be about ____________________ , not ________________." Select all options that are correct. population means, not sample means population variances, not sample means parameters, not statistics statistics, not parameters Question 3 Background : Longevity ~ Presidents, Popes, Monarchs The table below lists the number of years that U.S. presidents, popes, and British monarchs (since 1690) lived after their inauguration, election, or coronation, respectively. As of this writing, the last president is Gerald Ford, the last pope is John Paul II, and the last British monarch is George VI. (Table is based on data from ComputerInteractive Data Analysis, by Lunn and NcNeil.) These data will be used to assess if, on average, presidents, popes, and British monarchs live the same number of years since their inauguration, election, or coronation, respectively; for the populations of all such presidents, popes, monarchs (past, present, and future). Question 3 Subquestions 3.a 0.5 point(s) Which of the following graphical displays should be used to check the ANOVA assumption that each population has a normal distribution? 4/9 4/6/2016 Three QQ plots (one for each group) One QQ plot (for all the data combined) Three box plots (one for each group) One box plot (for all the data combined) 3.b 1 point(s) Based on the ANOVA table, the p-value is 0.05058. Therefore our statistical decision for the test of the ANOVA null hypothesis at the 10% level of significance, and the appropriate conclusion in context should be: Reject H0 and conclude that, on average, presidents, popes, and British monarchs live the same number of years since their inauguration, election, or coronation, respectively (for the populations represented by these data). Reject H0 and conclude that, on average, at least one of presidents, popes, or British monarchs do not live the same number of years since their inauguration, election, or coronation, respectively (for the populations represented by these data). Fail to reject H0 and conclude that, on average, presidents, popes, and British monarchs live the same number of years since their inauguration, election, or coronation, respectively (for the populations represented by these data). Fail to reject H0 and conclude that, on average, at least one of presidents, popes, and British monarchs do not live the same number of years since their inauguration, election, or coronation, respectively (for the populations represented by these data). 3.c 1 point(s) 5/9 4/6/2016 One of the assumptions of ANOVA is that the population variances are equal. If they are equal, they equal some common value. Give an estimate of the common population variance. 838.5 9843.0 419.27 134.84 3.d 0 point(s) Here is a summary of the longevity measurements. Use the ANOVA and these summary results to construct a 95% confidence interval for the mean number of years that all U.S. Presidents live after their inauguration. Be sure to write the appropriate formula, clearly state the value of each quantity to be plugged into the formula, and perform the computations and provide the answer (including units). Student answer No answer entered. 3.e 0 point(s) A follow-up multiple comparisons analysis has been performed, using Tukey's procedure. The resulting table is provided. Select the pair(s) of categories that show significant difference. Pope vs. Monarch 6/9 4/6/2016 President vs. Monarch President vs. Pope Question 4 Background : Corn Production As part of an agriculture experiment, data on the number of corn plants growing in randomly sampled rows (a 17ft by 5-inch strip) for three different types of plots; 1 = sludge, 2 = spring disk, 3 = no till. You are asked to help conduct an ANOVA, using a 5% level of significance, to assess whether the population mean number of plants for each plot type are equal. The data for this study are provided in the file corn.Rdata (https://pbjcoursework.s3.amazonaws.com/Intro%20to%20Statistics/instructor/3-30-2016/17_14_725-corn.RData). Question 4 Subquestions 4.a 0.5 point(s) Based on the three R outputs below, is it reasonable to assume that the population variances for number of corn plants for the three types of plots are the same? State Yes or No for your overall determination and then provide three detailed statements (#1, #2, and #3; corresponding to each of the outputs) supporting your decision. Student answer No answer entered. 4.b 1 point(s) Which of the following is the appropriate null hypothesis that the Levene's test is designed to assess? 7/9 4/6/2016 Choice (i) Choice (ii) Choice (iii) Choice (iv) 4.c 1 point(s) Use R Commander to produce the ANOVA table for testing the equality of the population mean number of corn plants for the three different types of plots. Make sure to include your R output by copying and pasting your output below (or adding it in as an image). Then below the output, separately report the value of the test statistic and its corresponding p-value. Student answer No answer entered. Question 5 Background : Stats 250 GTD and NTS data Exploring Data Hands-On: You get to explore a de-identified Stats 250 dataset from the F15 term with the following variables for 1857 students: (1) finalgrade = final course percentage (using the max of two methods), (2) gtdused = the number of Get Things Done (GTD) Lists used (a list used consists of checking at least one of the list items) (3) gtdstatus = Get Things Done (GTD) Lists user status (0 = non-user, 1 = user) (4) ntsused = the number of Name That Scenario (NTS) practice sessions performed (a practice session consists of completing a set of 10 scenarios) (5) ntsstatus = Name That Scenario (NTS) user status (0 = non-user, 1 = low-level user, 2 = high-level user) You are asked to use R and R Commander to explore this data. The dataset is called STATS250DATAF15.Rdata (https://pbj-coursework.s3.amazonaws.com/Intro%20to%20Statistics/instructor/3-30-2016/17_59_407STATS250DATAF15.RData). 8/9 4/6/2016 Question 5 Subquestions 5.a 0.5 point(s) First state the research question you would like to explore. Here are a few examples, but you are welcome to come up with your own. How does final course performance compare (on average) for different levels of NTS users? Compare the mean final course performance for different NTS user groups for GTD users only, or for non-GTD users only. How does final course performance compare (on average) for different GTD list users? Is there a relationship between final course performance and NTS usage? between final course performance and GTD list usage? between NTS usage and GTD list usage? Student answer No answer entered. 5.b 1 point(s) Provide at least one graphical summary (as .jpg, .jpeg, or .png) and some appropriate numerical summaries from your data exploration that aligns with your research question. Include a few sentences to comment about what the graph or numerical summaries show. Student answer No answer entered. 5.c 1 point(s) Perform an appropriate statistical analysis that aligns with your research question (e.g., ANOVA, twoindependent samples t test or confidence intervals, regression analysis, etc). Provide the R output and a 2-3 sentence summary of your results. Student answer No answer entered. Edit Assignment (/#!/students/56f7259a2022c90b000a6898/do) 57050c98786f4a0b00d4d16a 9/9