##################>### ############################################# #################### R#o#o#t# #E#n#t#r#y############################################################## ###################h ######@#######W#o#r#k#s#h#e#e#t#D#a#t#a#1#7################################## # ##################################################W#o#r#k#s#h#e#e#t #I#n#f#o#################################################################### ##############################C#o#m#p#r#e#s#s#e#d############################## ###########################################h ##h ############################################## ### ### ########################################################################## ### ############ ###WORK###############@###\\#\\#u#d#r#i#v#e#.#w#i#n#.#p#s#u#.#e#d#u#\\#U#s#e#r#s#\\ #w#\\#a#\\#w#a#z#1#0#7#\\#D#e#s#k#t#o#p#\\#F#a#c#e#b#o#o#k#G#e#n#d#e#r#.#M#T#W#4#### ###########F#a#c#e#b#o#o#k#G#e#n#d#e#r#.#M#T#W################################# ############################################# ### ######### @ ###############S#e#g#o#e# #U#I#2###############S#e#g#o#e# #U#I# #S#e#m#i#b#o#l#d#################*######ADDR#### ###CmColumnVar#ADDR#### ###CmColumnVar###################################################| ###############################\\###########################@################### ######################################################################### ################_########################################################## ############;###dFj#j#pn#fo #bgAh>'3"\\ h6Y3Z#,#v##qK#<#zg#H##s#2#X3b0#kit/t{:"##@ #@g`t#z@0t z`4@zp: =@#z=P# ###Z#####@@i@`bM3@{p=#:b~###N##|#:P:`:p5 u#j#V##~#R#T#VR|@`wa6#'KSS[#B =[qb#h#\\>hq #G#HL4w#;s#>#E#6t#H!M#\\8qwV8}#J#Zrjq e###p7}_/N-h#[#psv#6u,~L[s:#;;#/DE3#?]K#Gg)? k[jA"y#R#H=$y>EtY@ #v#vc#;#r~w|#-1M?%3##v% #!=##y|{XF6#%%)Im~zL~"*6#<=SSp )h{#O6O#7IO#hN#S/]O8~Ag'5O x*y^#Ng#yWQ/)No##8^? tt#O)#)#8^ns:##y#T [ vN#e#s|[ 8^n[ Ot;#^z{>m> C#azF49z##W,,<.0|M)_Z]9_;rUK;2#;#)y#n,O$=KX>|#v#f#|I\\ t'4"~+################################################################## ################################################################################ ################################################################################ ################################################################################ ################################################################################ ##################################################################### Lesson 9: Inference for Two Samples Due Monday, October 30, 11:59PM ET NAME: Answer the following questions showing all work. Full credit will not be given to answers without work shown. If you use Minitab Express or StatKey include the appropriate output (copy + paste). If you do hand calculations show your work using the Word equation editor. Clearly identify your final answers. Output without explanation will not receive full credit and answers with no output or explanation will not receive full credit. Round all answers to 3 decimal places. If you have any questions, post them to the course discussion board. 1. Market researchers working for a large fitness company want to know if male and female patrons differ in terms of how many hours per week they spend at the gym. At their gym, customers have ID cards that they use to sign in and out of the gym, so the researchers are able to obtain data concerning how long each customer was in the gym. They obtain data from a random sample of 50 male patrons and 50 female patrons. [30 points] A. What is the independent variable? B. What is the dependent variable? C. Is the dependent variable categorical or quantitative? Explain why. D. Are the two groups (males and females) independent or paired? Explain why. E. Write the null and alternative hypotheses that the researchers should be testing. Use the Equation Editor in Word and the correct notation. F. What type of graph could the researchers make to display their data? Explain why. G. What method of constructing a sampling distribution should the researchers use (e.g., randomization, t distribution, z distribution)? Explain why. 2. At the beginning of the Summer 2017 semester a random sample of Penn State students enrolled in online sections of STAT 200 were surveyed and asked for their employment status and primary campus. These data are presented in the contingency table below. [35 points] Employment Status Full Time Less Than Full Time Primary Campus World Campus Physical Campus 27 12 11 34 A. What proportion of World Campus students in this sample were working full time? Lesson 9: Inference for Two Samples Due Monday, October 30, 11:59PM ET B. What proportion of students in this sample who typically attend a physical campus were working full time? C. Use the five-step hypothesis testing procedure to determine if the proportion of World Campus students who were working full time is different from the proportion of students from physical campuses who were working full time. If assumptions are met, use the normal approximation method. Do not do any calculations by hand. Use Minitab Express and remember to include all relevant output. Step 1: Check assumptions and write hypotheses Step 2: Calculate the test statistic Step 3: Determine the p-value Step 4: Decide between the null and alternative hypotheses Step 5: State a real world conclusion D. Are your results in part C practically significant? Explain why or why not. E. Construct a 95% confidence interval for the difference in the proportion of World Campus students and students who typically attend a physical campus who are working full-time. Show how you checked assumptions. If assumptions are met, use the normal approximation method. Do not do any calculations by hand. Use Minitab Express and remember to copy+paste all relevant output. 3. Researchers are studying gender differences in Facebook users. They want to know if American men and women differ in terms of how many friends they have on average. Data were collected from a random sample of 130 Facebook users from the United States. Data concerning their genders and number of Facebook friends are in the file FacebookGender.MTW. [35 points] A. Construct a graph to compare the number of Facebook friends that men and women in this sample have. B. Use the five-step hypothesis testing procedure to determine if there is evidence that in the population of all American Facebook users men and women differ in terms of the number of Facebook friends they have on average. If assumptions are met, use a t distribution to approximate the sampling distribution. Do not do any calculations by hand. Use Minitab Express and remember to include all relevant output. Step 1: Check assumptions and write hypotheses Step 2: Calculate the test statistic Step 3: Determine the p-value Step 4: Decide between the null and alternative hypotheses Step 5: State a real world conclusion C. Construct a 95% confidence interval to estimate the mean difference in the number of Facebook friends that men and women have in the population of all American Facebook users. Do not do any calculations by hand. Use Minitab Express and remember to copy+paste all relevant output. Lesson 9: Inference for Two Samples Due Monday, October 30, 11:59PM ET D. In StatKey, use bootstrapping methods to construct a 95% confidence interval for the differences in means. Copy+paste your output here. E. Why are your results in parts C and D slightly different