3.1 Comparison between 24-hour gas station and 18-hour gas station Use two-datas

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3.1 Comparison between 24-hour gas station and 18-hour gas station

Use two-dataset t test for independent processes with unequal variances to compare mean of gallons sold by 24-hour gas station and that by 18-hour gas station (degrees of freedom = 53). 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. A station that operates 24 hours a day is indicated when HOURS=1; HOURS=0 for those open 18 hours per day.

GALLONS(Hours=0) GALLONS(Hours=1) 100967 114697 100714 163445 96067 69216 60305 120872 90534 151701 106491 112633 146435 203192 95883 118505 155904 66051 133815 144336 119287 148071 119046 102362 87284 125291 121615 151394 106435 162777 87453 93153 179159 189206 97689 84663 125342 169497 72907 128828 141562 Average 113118    110,166.60 134355 119172 Standard Dev 173902     28,385.72 106367 123414 110968 136465 128252 152485 109158 107604 229404 160639 102154 165124 97797 251346 186091 124854 131587 194732 175054 140357 139911 157679 277823 151809 150464 154559 156151 115560 152842 153472 185860 140529 129997 192850 141361 148093 163568 213409 231592 155271 128626 181823 169513 192564 135808 275438 256209 170729 194222 110244 166050 93565 131137 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           167,334.59 St Dev             70,175.13

Explanation / Answer

Null and alternate hypothesis are

P(T<=t) two-tail

Reject null hypothesis.

Null and alternate hypothesis are

Reject null hypothesis

There are sufficient evidence to conclude that average monthly fuel sale of gas station opened for 24 hours is greater than the average monthly fuel sale of gas station opened for 18 hours.

t-Test: Two-Sample Assuming Unequal Variances GALLONS(Hours=0) GALLONS(Hours=1) Mean 110166.6 167334.5872 Variance 805749226 4924548655 Observations 20 172 Hypothesized Mean Difference 0 df 53 t Stat -6.886282107

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