Question

A retailer wants to see if a red "Sale" sign brings in less revenue than the same "Sale" sign in blue. The data below shows the revenue in thousands of dollars that was achieved for various days when the retailer decided to put the red "Sale" sign up and days when the retailer decided to put the blue Sale sign up. Red: 2.1, 3.4, 3.9, 2.5, 3.3.2.4. 2.4. 2.9. 1.2 2.9 Blue: 3, 62, 43, 43, 48, 3.4, 2.9, 2.1, 3.1, 3.2 Assume that both populations follow a normal distribution. What can be concluded at the a-0.01 level of significance level of significance? For this study, we should use Select anar a. The null and alternative hypotheses would be: Hot e ct an aner Select an answer b. The test statistie - (please show your answer to 2 decimal places.) c. The p-value (Please show your answer to decimal places) d. The p-value is? Do e. Based on this, we should select an answer the null hypothesis. Thus, the final conclusion is that ... The results are statistically insignificant -001. so there is an evidence to conclude that the population mean revenue on days with a red "Sale" align is less than the population mean revenue on days with a blue "Sale" sin The results are statistically significant at -0.01, so there is sufficient evidence to conclude that the mean revenue for the ten days with a red "Sale" sign is less than the mean revenue for the ten days with a blue Salesian The results are statistically significant -0.01, so there is sufficient evidence to conclude that the population mean revenue on days with a red "Sale" sign is less than the population mean revenue on days with a blue "Sale" sig The results are statistically insignificant -0.01, so there is statistically significant evidence to conclude that the population mean revenue on days with a red "Sale" sinis equal to the population mean revenue on days with a blue Sale sign Interpret the p-value in the context of the study There is a 1.73% chance that the mean revenue for the 10 days with a red "Sale" sign is at least I thousand dollars less than the mean revenue for the 10 days with a blue "Sale" If the population mean revenue on days with a red "Sale" in is the same as the population mean revenue on days with a Mue"Sale" sign and if another 10 days with a red Sales and 10 days with a blue Sale sign are observed then there would be a 1.73% chance that the mean revenue for the 10 days with a red "Sale" sign would be at least I thousand dollar less than the mean revenue for the 10 days with a Wue Salesign If the umple mes revenue for the 10 days with a red "Salon is the w eathe ample revenue for the 10 days with a blue Sales and if necher 10 days with a red "Sale" sign and 10 days with a blu"Sale" si are observed then there would be a chance of concluding that the revenue for the 10 days with a red Sales is at least I thousand dollars less than the mean revenue for the 10 days with a bla "Salesi There is a 1.71% chance of Type I error

Answer 1

dof (si/nissing) | | E - 1 5 -1

For this study, we should use two – sample t - test with unequal variances. a. Ho: Mi = 42; 1: red, 2: blue H:Hi<H2 - T1 - T2 6. Test statistics : - , where īı = 2.7, 72 = 3.73, / s . 53 Vnin2 si = 0.76, 52 = 1.18; n1 = n2 = 10, dof = 15( from standard formula above) Test statistic := -2.32 c. p-value = P(t < -2.32) = 0.0173 d. p - value is >a. e. Based on this, we should ACCEPT the null.

f. The final conclusion is that.. Correct option : 1st choice i.e. "The results are statistically ... insignificant ..., so there is insufficient evidence to conclude .... is less than.....” g. Correct option : 2nd choice. If the population mean ..... and if another 10 ..... then there would be a 1.73% chance that the mean revenue for ... would be at least 1 thousands dollars less than the mean revenue ....sign.