Question

(1 point) Ken and Billy both live in the same neighborhood, and work at the university. Ken drives to work, Billy rides his bicycle. You - a budding statistician - have been asked to settle an argument. Ken believes that more often than not, his commuting time via his drive is less than Billy's. Billy believes that this is not so, due to traffic volume and traffic lights. Over the period of one month, the statistician randomly selects eight days for Ken and eight days for Billy. On each day, they will be asked to measure, to the nearest tenth of a minute, the amount of time it takes them to get from their home to the university campus. The commuting times are given on each randomly chosen day, for each person. Ken: 12.7, 16.8, 6.9, 8.4, 5, 11.3, 18.1, 12.4; Billy: 21.5, 18.2, 20.7, 18.4, 18.5, 18.5, 19.1, 19.2; Download.csv file Carry out a statistical test, the results of which will be used to settle Ken and Billy's argument. (a) Using the technology available to you, visually and statistically inspect this data. From this, construct the most appropriate statistical hypotheses. A. H : Kon = Dilly HA: Ken + Dilly B. H : Ken - ÜBilly HA: Ken 7 Billy C. H, ID - 0 HAUD 70 D. H : HD - 0 HAJD <0 E. H, : Km = Billy H Ken > Billy F. H: Ken - Dilly HA: MKon < Dilly G. H: Up = 0 HA:M >0 он. Н, : йжеn = йваllу на: йдеn <йваllу 1. Ho : Ken = Billy HA: Ker > Billy (b) Find the value of the test statistic for this test, use at least one decimal in your answer. Test Statistic = (c) Determine the P-value of your statistical test in part (c), and report it to at least three decimal places. P= (d) At a = 0.05, this data indicates that you will ? the null hypothesis. You can tell Ken that his commute time is ? Billy's.

Answer 1

501?? ..n,=42=8 ken for For Billy, (Yi-72 (Xi-8) 2 yo 21.5 18-2 20-7 18-4 xi 127 11.5625 16:8 28.6225 6.9 2017025 8.4 19.3025 416025 0.0225 uu.2225 12.4 0.9025 Taal = 9106 146.94 18.5 195 19:1 14.2 11.3 18.1 5.006406 1:128906 2.066406 0.743906 0.581406 0.581406 0-026406 8.003906 1140-9)= 10.13875 24:2146194 n T= I * = 9161.45 =11.45) 9 = F - 14694 = 19.2625 » 9 = 1926257 s? I [ Elxix®)?+ [141-9)2) = 11.21991 ni tn -2 - 52-11.21991 , S = 3.349614. suppose average time for ken = Mken 1 " " Billy - Meille Test af hypothesis: Ho: Mken = M Billy Vs Hi Meen < MBilly (one failed) option: F is correct; Scanned with CamScanner

Under Ho: test statistic TT tas sbitha in th=2 . Then -6.00069 value of test statistic -10.05 1. t= 116 74807 It=-610) Ans. is one (since test failed ) then þ- valle twt4 p-value = pita-60) -0.0000 Tb-value - 0.000 I Ansi a Atx=0.05 since p-value is less than a so we reject the hull hypothesis. So we can say that ken that this commute time is less than Bill's. Scanned with CamScanner