3.2 Comparison between gas station with car wash on site and gas station without
ID: 3358676 • Letter: 3
Question
3.2 Comparison between gas station with car wash on site and gas station without car wash on site
Use two-dataset t test for independent processes with unequal variances to compare mean of gallons sold by gas station with car wash on site and that by gas station without car wash on site (degrees of freedom = 5). First, do a two-tailed test. Then, based on your conclusion for the two-tailed test, you decide whether a follow-up one-tailed test is needed. If yes, also do the one-tailed test and summarize your conclusion. In each of the two tests, you must formulate null and alternative hypotheses, decide significance level, calculate test statistic and p-value, and summarize statistical conclusions.
GALLONS is the average monthly fuel sales (both gasoline and diesel) in number of gallons.
CARWASH is 1 if the station has a car wash on site and 0 if not.
GALLONS(Carwash=0) GALLONS(Carwash=1) 114697 139911 163445 192850 69216 231592 100967 169513 120872 275438 151701 72907 112633 100714 Average 203192 180,368.50 96067 118505 St Dev 66051 70,880.84 60305 144336 148071 102362 125291 151394 162777 93153 189206 84663 169497 128828 141562 113118 134355 119172 173902 106367 90534 123414 106491 110968 136465 128252 152485 109158 107604 229404 146435 160639 95883 102154 165124 97797 251346 186091 124854 131587 194732 175054 140357 157679 277823 155904 151809 150464 154559 156151 115560 152842 133815 153472 185860 119287 140529 129997 141361 148093 163568 213409 155271 128626 181823 192564 135808 256209 170729 194222 119046 87284 121615 106435 87453 110244 166050 93565 179159 131137 97689 125342 125947 324049 144502 370774 204132 192684 343020 127770 91359 113865 119219 132316 145490 270821 194330 132368 420904 106618 342251 160447 129956 133935 147899 172422 129794 125602 110978 243723 77580 96678 149398 225170 193951 203392 86758 228659 95964 147958 82515 158866 76103 80374 165755 129052 117422 243341 183087 181567 169198 81390 126188 138759 112970 137558 107985 118438 214032 126762 161782 95000 369822 181984 140814 381807 220070 348662 276852 271942 230982 117174 500607 187112 283747 97538 112651 151770 119360 103406 232166 194772 182023 171902 257530 214396 200472 97363 227323 221886 215838 169311 136999 289523 175550 172789 Average 160,767.04 St Dev 69,305.75Explanation / Answer
p-value = 0.5342
As p-value is greater than significance level of 0.05, we failed to reject null hypothesis.
This means there are not sufficient evidences to conclude that two processes mean are different.
There is no need to perform 1 tailed test
x1(bar) 160767.04 x2(bar) 180368.50 s1 69305.75 s2 70880.84 n1 186 n2 6 SE = sqrt[ (s12/n1) + (s22/n2) ] (s12/n1) 25824123.5649 (s22/n2) 837348913.1843 SE 29379.8066Related Questions
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