Question

You own a company that sells high-end motorcycles. You are considering launching a new marketing campaign in an attempt to increases sales but you are unsure of when you should start it. You believe it makes the most sense to market more when the fewest number of people typically buy motorcycles. So, you decided to use your quarterly sales data from the past 2+ years to test to see if there is a difference in sales between the quarters and if so, which quarter had the lowest sales.

For this question, you will need to download the Sales Data and then use the data analysis tool pack in Excel to run an Anova: Single Factor Test. Note, you will need to install the data analysis tool pack on your computer. How to do this differs based on the type of computer you are using, but instructions can be found on google for both Mac and PC.

Sales Data: https://arizona.grtep.com/core/uploadfiles/components/283631/files/Sales%20Data.xlsx

How many pair-wise comparisons or Fisher’s confidence intervals would you need to calculate in order to compare all of the quarters versus one another? (i.e. Quarter 1 versus Quarter 2 is one pair. Quarter 1 versus Quarter 3 is another pair.)

From the ANOVA output, enter the following. Round your answers to 4 decimals.

F = Test Statistic =

F crit = critical value =

p-value =

df₂ = n_T – c =

Mean Square Error (MSE) =

Calculate a 95% Fisher’s confidence interval between Quarter 1 and Quarter 2. Let Quarter 1 be population 1 and Quarter 2 be population 2 in the formula. Round your answer to 2 decimals.

Calculate a 95% Fisher’s confidence interval between Quarter 1 and Quarter 3. Let Quarter 1 be population 1 and Quarter 3 be population 2 in the formula. Round your answer to 2 decimals.

Answer 1

(a)
One factor ANOVA
	Mean	n	Std. Dev
	87.6	266	66.54	Sales in Qtr 1
	87.2	243	73.11	Sales in Qtr 2
	68.2	183	72.36	Sales in Qtr 3
	88.8	184	86.47	Sales in Qtr 4
	83.7	876	74.40	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	55621.5788	3	18540.5263	3.3765	.0179
Error	4788179.1917	872	5491.0312
Total	4,843,800.77	875

F Critical =

2.6151

(b) We would need C(4, 2) = 6 comparisons

(c)    

For quarter 1 and quarter 2, x1-bar - x2-bar = 87.6 - 87.2 = 0.4

Width of the 95% confidence interval = (t(0.025), dfE) * √[MSE * {(1/n1) + (1/n2)}] = (t(0.025), 872) * √[5491.031 * {(1/266) + (1/243)}] = 1.9627 * 6.5757 = 12.9061

The 95% confidence interval is [0.4 - 12.9061, 0.4 + 12.9061] = [-12.51, 13.31]

For quarter 1 and quarter 3, x1-bar - x3-bar = 87.6 - 68.2 = 19.4

Width of the 95% confidence interval = (t(0.025), dfE) * √[MSE * {(1/n1) + (1/n2)}] = (t(0.025), 872) * √[5491.031 * {(1/266) + (1/183)}] = 1. * 1.9627 * 7.1168 = 13.9681

The 95% confidence interval is [19.4 - 13.9681, 19.4 + 13.9681] = [5.43, 33.37]