Question

A retailer wants to see if a red "Sale" sign brings in more 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: 1, 3.6, 3.6, 3.2, 3.4, 3.8, 3.1, 1.5, 3.6 Blue: 0.5, 1.9, 1.6, 2.9, 2.1, 2.9, 1.2, 2.2, 2.9, 3.8 Assume that both populations follow a normal distribution. What can be concluded at the α = 0.05 level of significance level of significance? For this study, we should use The null and alternative hypotheses would be: H 0 : (please enter a decimal) H 1 : (Please enter a decimal) The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is α Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The results are statistically insignificant at α = 0.05, so there is insufficient evidence to conclude that the population mean revenue on days with a red "Sale" sign is more than the population mean revenue on days with a blue "Sale" sign. The results are statistically insignificant at α = 0.05, so there is statistically significant evidence to conclude that the population mean revenue on days with a red "Sale" sign is equal to the population mean revenue on days with a blue "Sale" sign. The results are statistically significant at α = 0.05, so there is sufficient evidence to conclude that the mean revenue for the nine days with a red "Sale" sign is more than the mean revenue for the ten days with a blue "Sale" sign. The results are statistically significant at α = 0.05, so there is sufficient evidence to conclude that the population mean revenue on days with a red "Sale" sign is more than the population mean revenue on days with a blue "Sale" sign. Interpret the p-value in the context of the study. If the sample mean revenue for the 9 days with a red "Sale" sign is the same as the sample mean revenue for the 10 days with a blue "Sale" sign and if another 9 days with a red "Sale" sign and 10 days with a blue "Sale" sign are observed then there would be a 5.29% chance of concluding that the mean revenue for the 9 days with a red "Sale" sign is at least 0.8 thousand dollars greater than the mean revenue for the 10 days with a blue "Sale" sign There is a 5.29% chance of a Type I error. There is a 5.29% chance that the mean revenue for the 9 days with a red "Sale" sign is at least 0.8 thousand dollars greater than the mean revenue for the 10 days with a blue "Sale" sign. If the population mean revenue on days with a red "Sale" sign is the same as the population mean revenue on days with a blue "Sale" sign and if another 9 days with a red "Sale" sign and 10 days with a blue "Sale" sign are observed then there would be a 5.29% chance that the mean revenue for the 9 days with a red "Sale" sign would be at least 0.8 thousand dollars greater than the mean revenue for the 10 days with a blue "Sale" sign. Interpret the level of significance in the context of the study. If the population mean revenue on days with a red "Sale" sign is the same as the population mean revenue on days with a blue "Sale" sign and if another 9 days with a red "Sale" sign and 10 days with a blue "Sale" sign are observed, then there would be a 5% chance that we would end up falsely concluding that the sample mean revenue for these 9 days with a red "Sale" sign and 10 days with a blue "Sale" sign differ from each other. There is a 5% chance that green is your favorite color, so why woud you even consider red or blue? There is a 5% chance that there is a difference in the population mean revenue on days with a red "Sale" sign and on days with a blue "Sale" sign. If the population mean revenue on days with a red "Sale" sign is the same as the population mean revenue on days with a blue "Sale" sign and if another 9 days with a red "Sale" sign and 10 days with a blue "Sale" sign are observed then there would be a 5% chance that we would end up falsely concluding that the population mean revenue for the days with a red "Sale" sign is more than the population mean revenue on days with a blue "Sale" sign

Answer 1

For Red :

∑x = 26.8

∑x² = 87.98

n1 = 9

Mean , x̅1 = Ʃx/n = 26.8/9 = 2.9778

Standard deviation, s1 = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(87.98-(26.8)²/9)/(9-1)] = 1.0109

For Blue :

∑x = 22

∑x² = 56.78

n2 = 10

Mean , x̅2 = Ʃx/n = 22/10 = 2.2000

Standard deviation, s2 = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(56.78-(22)²/10)/(10-1)] = 0.9649

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Null and Alternative hypothesis:

Ho : µ1 = µ2

H1 : µ1 > µ2

df = ((s1²/n1 + s2²/n2)²)/[(s1²/n1)²/(n1-1) + (s2²/n2)²/(n2-1) ] = 16.586 = 17

Test statistic:

t = (x̅1 - x̅2)/√(s1²/n1 + s2²/n2) = (2.9778 - 2.2)/√(1.0109²/9 + 0.9649²/10) = 1.711

p-value :

Right tailed p-value = T.DIST.RT(1.7109, 17) = 0.0526

Decision:

p-value > α, Do not reject the null hypothesis

Conclusion:

The results are statistically insignificant at α = 0.05, so there is insufficient evidence to conclude that the population mean revenue on days with a red "Sale" sign is more than the population mean revenue on days with a blue "Sale" sign.

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Interpret the p-value in the context of the study.

If the population mean revenue on days with a red "Sale" sign is the same as the population mean revenue on days with a blue "Sale" sign and if another 9 days with a red "Sale" sign and 10 days with a blue "Sale" sign are observed then there would be a 5.29% chance that the mean revenue for the 9 days with a red "Sale" sign would be at least 0.8 thousand dollars greater than the mean revenue for the 10 days with a blue "Sale" sign.

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Interpret the level of significance in the context of the study:

There is a 5% chance that there is a difference in the population mean revenue on days with a red "Sale" sign and on days with a blue "Sale" sign.