Question

The owner of chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. Sales can vary considerably depending on the day of the week and the season of the year, so she decides to eliminate such effects by making sure to record each store's sales on the same sample of days. After choosing a random sample of 8 days, she records the sales (in dollars) for each store on these days, as shown in Table 1 Difference Store 2 (Store 1 Store 2) Store 1 Day 451 330 1 781 970 822 148 525 402 123 3 4 219 159 60 329 253 76 500 6 150 350 720 7 941 221 527 126 401 Table 1 Based on these data, can the owner conclude, at the 0.10 level of significance, that the mean daily sales of the two stores diiffer? Answer this question by performing a hypothesis test regarding (which is u with a letter "d" subscript), the population mean daily sales difference between the two stores. Assume that this population of differences (Store 1 minus Store 2) is normally distributed. Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

Answer 1

let de stores - storz Based on given data - sample size n=81 o paired mean t a - Edi/n = 1434 Td = 179.25 e Sample variance St= 5 (di-xas 52= • Sample std dis = 85481.5 12.211.6429 6 = V1 2211-6429 5 =_110.5063 To test • Null Hypothesie Ho: Md = 0 v • Altmative Hypothesis He: lla Fo Type of test statistics is I with I degress of fidecom Test statistics is to Xd-ld SIJA

179.25-0 110.5063/18 t= 4.5879 4.580 V to Critical values = = + tq12,0-) I toros ? -> a=0.1 = - - 1895 + 1.8946 & 1.895 v stones At 2=0.10 $ Répest Ho Conclusion: man daily sales of two differs Answer is yes ✓