Stat 305 (Fall 2016): Homework 2 Due Date: Thursday, September 8, in class Write legibly and show all your work. Please staple your assignment if you use more than one sheet. 1. The accompanying data are three hypothetical samples of size 10 that are supposed to represent measured manganese contents in specimens of 1045 steel (the units are points, or 0.01%). Suppose that these measurements were made on standard specimens having \"true\" manganese contents of 80, using three different analytical methods. (Thirty different specimens were involved.) Method 1 Method 2 Method 3 87 86 84 74 85 83 78 82 78 81 87 79 78 85 85 77 84 82 84 84 82 80 82 81 85 82 82 78 85 79 (a) Fill out the following table (Table 1) for quantiles of manganese contents in specimens of 1045 steel. i0.5 (Note that, Q1 ( i0.5 10 )= ith smallest data point for method 1, Q2 ( 10 )= ith smallest data point for i0.5 method 2, and Q3 ( 10 )= ith smallest data point for method 3.) Table 1: Quantiles of the manganese content distribution in specimens of 1045 steel i 1 2 3 4 5 6 7 8 9 10 Q1 ( i0.5 10 ) 74 i0.5 10 0.05 Q2 ( i0.5 10 ) 82 Q3 ( i0.5 10 ) 78 (b) Compute the sample range and IQR for each method. (c) Compute the sample mean, median and standard deviation for each method. (d) Discuss the effectiveness of the three analytical methods in terms of the numerical summaries in Parts (a) (c) and in terms of the concepts of accuracy and precision discussed in Section 1.3. 2. The accompanying values are the lifetimes (in numbers of 24 mm deep holes drilled in 1045 steel before tool failures) for n = 12 D952-II (8 mm) drills. These were read from a graph in \"Computer-assisted Prediction of Drill-failure Using In-process Measurements of Thrust Force\" by A. Thangaraj and P. K. Wright (Journal of Engineering for Industry, May 1988). (A data set called HW2-lifetimes.jmp can be found on Blackboard.) 47 145 172 86 122 110 172 52 194 116 149 48 (a) Construct a histogram and a stem-and-leaf plot for the data using JMP. (b) Report the sample mean, median and standard deviation from the JMP output. (c) Compute and report the sample range and IQR from the JMP output. 1 Stat 305 (Fall 2016): Homework 2 Due Date: Thursday, September 8, in class (d) Make a Normal QQ plot for this data using JMP. Would you describe this distribution as bell-shaped? Why or why not? Follow the steps below to use JMP to obtain a histogram, stem-and-leaf plot, normal QQ plot and summary statistics for the distribution of the lifetimes for the 12 drills. With the data set open in JMP, click on Analyze Distribution. Select the variable lifetime in the Select Columns box by clicking on it once. The variable should be highlighted in blue. Click on the Y, Columns box, followed by the OK button. You should now have a histogram and the summary statistics for the variable lifetime. To change the display of the histogram to a horizontal layout, click on the red triangle next to the variable name lifetime and select Display Options Horizontal Layout. To add a count axis to the histogram, click on the red triangle next to the variable name lifetime and select Histogram Options Count Axis. The boxplot for the variable lifetime is placed just above the histogram. To obtain a stem-and-leaf-plot, click on the red triangle next to the variable name lifetime and select Stem and Leaf. To obtain a Normal QQ plot, click on the red triangle next to the variable name lifetime and select Normal Quantile Plot. Steps to save the JMP output as an image file, such as a .png or .jpg file. on a Mac: With the output window open in JMP, press and hold (IN ORDER) - COMMAND SHIFT 4. A cross hair tool will come up. You can take a custom screenshot that will go directly to the Desktop. on a PC: With the output window open in JMP, click Alt + F followed by S to save the file. Make sure to save the file as a .png or .jpg, for example, but not as a .jrp file! 3. Presidential Election (cont'd). This fall the United States will elect its 45th president. The Republican and Democratic party presidential hopefuls have been campaigning relentlessly in an effort to not only become their party's nominee but also become elected the next president of the United States. The election in November could be as historic as the election in 2008 if the country elects its first woman to be president. A political scientist working for NORC (National Opinion Research Center) is conducting a study of public opinion among registered voters on favorability of a female president. She obtains a representative sample consisting of 1254 registered voters, 68% of which believe that the country is ready for a female president. For each of the following questions, select the best answer from choices i. through vi. listed below. i. all registered voters in the U.S. ii. the 1254 registered voters participating in the study iii. the percentage of the 1254 registered voters who believe that a female president is acceptable iv. all registered voters who believe that a female president is acceptable v. the percentage of all registered voters who believe that a female president is acceptable vi. all eligible voters in the U.S. (a) What is the parameter? (b) What is the statistic? 2 Stat 305 (Fall 2016): Homework 2 Due Date: Thursday, September 8, in class 4. Chapter 3 Exercises, page 116: #8. (A data set called HW2-compound.jmp can be found on Blackboard.) (Note: For Part (c), back-to-back stem-and-leaf plots are not available in JMP, so you have to do this by hand.) Follow the instructions below to use JMP to obtain a side-by-side boxplot. With the data set open in JMP, click on Analyze Fit Y by X. Select the variable Failure Time in the Select Columns box by clicking on it once. The variable should be highlighted in blue. Then click on the Y, Response box. Select the categorical variable Compound in the Select Columns box by clicking on it once. The variable should be highlighted in blue. Then click on the X, Factor box followed by the OK button. You should now have a graph with the data points separately for the two compounds. To obtain a boxplot, click on the red triangle next to Oneway Analysis of Failure Time By Compound and select Display Options Box Plots. To obtain the summary statistics for each compound click on the red triangle next to Oneway Analysis of Failure Time By Compound and select Means and Std Dev. 3 ################################utf-8####Warning ####C#################7This data table had been saved in a more recent format.###########BIt is not compatible with the format known to this version of JMP.#Please do not save this table#####################################ASaving this table with this version of JMP will destroy the data.#####################a#########utf-8#########@}A##7###Apr 1 2015, 13:13:07, Release, JMP Pro, Version 12.0.1######################################################################## ################################################################################ ########################################################w#L##########F#N### ########t###U###{###v##################### #Failure Time## cc##############################> p=#@#Q##@ffffff#@"@ p= #@Q##)@fffff)@Q#k.@ p= 0@p= 0@Q# @ p= #@z#G#@#Q##@Gz##@(\\#@#Q##@*\\(#@> p"@#####)@##Compound## cc############################## #############?######?######?######?######?######?######?######?######? ######? #######@#######@#######@#######@#######@#######@#######@#######@#######@#######@ ################################utf-8####Warning ####C#################7This data table had been saved in a more recent format.###########BIt is not compatible with the format known to this version of JMP.#Please do not save this table#####################################ASaving this table with this version of JMP will destroy the data.##### ###############a#########utf-8#########}A##7###Apr 1 2015, 13:13:07, Release, JMP Pro, Version 12.0.1############>#############################~#J#####################i### i##########9#########lifetime## cc############################## ############G@##### b@#####e@#####U@#####^@#####[@#####e@######J@#####@h@######]@#####b@###### H@