Question

General guidelines:

Use EXCEL or PHStat to do the necessary computer work.

Do all the necessary analysis and hypothesis test constructions, and explain completely.

Read the textbook Chapter 11. Solve the textbook example on page 403, "Mobile Electronics," in order to compare four different in-store locations with respect to their average sales.

Use One-Way ANOVA to analyze the data set, data, given for this homework.

Use 5% level of significance.

1) Do the Levene test in order to compare the variance of the sales level at four different in-store locations.

2) If there are no significant differences between the variance of sales, then conduct the one-way ANOVA hypothesis test to compare the average sales level at four different in-store locations.

3) If you have seen evidence of difference among the average sales levels at these four different in-store locations, then identify which in-store locations have significantly different average sales than other in-store locations, by using the Tukey procedure

Data Set:

In-aisle Front Kiosk Expert 30.06 32.22 30.78 30.33 29.96 31.47 30.91 30.29 30.19 32.13 30.79 30.25 29.96 31.86 30.95 30.25 27.74 32.29 31.13 30.55 32 31 30 33 30.5 30

Answer 1

MINITAB used for analysis.

Use One-Way ANOVA to analyze the data set, data, given for this homework. Use 5% level of significance.

1) Do the Levene test in order to compare the variance of the sales level at four different in-store locations.

Test for Equal Variances: Inasile, front, kiosk, expert

Method

Null hypothesis	All variances are equal
Alternative hypothesis	At least one variance is different
Significance level	α = 0.05

95% Bonferroni Confidence Intervals for Standard Deviations

Sample	N	StDev	CI
Inasile	5	1.03403	(0.180537, 11.8340)
front	7	0.46824	(0.161813, 2.1066)
kiosk	8	0.35848	(0.094007, 1.9875)
expert	6	0.17646	(0.053434, 0.9983)

Individual confidence level = 98.75%

Tests

Method	Test Statistic	P-Value
Multiple comparisons	—	0.133
Levene	0.68	0.575

Calculated Levene test value = 0.68, P=0.575 which is > 0.05 level of significance. Ho is not rejected. We conclude that variance of the sales level at four different in-store locations are equal.

2) If there are no significant differences between the variance of sales, then conduct the one-way ANOVA hypothesis test to compare the average sales level at four different in-store locations.

One-way ANOVA: Inasile, front, kiosk, expert

Method

Null hypothesis	All means are equal
Alternative hypothesis	Not all means are equal
Significance level	α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor	Levels	Values
Factor	4	Inasile, front, kiosk, expert

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	3	21.606	7.2020	23.83	0.000
Error	22	6.648	0.3022
Total	25	28.254

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
0.549694	76.47%	73.26%	65.06%

Means

Factor	N	Mean	StDev	95% CI
Inasile	5	29.582	1.034	(29.072, 30.092)
front	7	32.139	0.468	(31.708, 32.569)
kiosk	8	30.758	0.358	(30.354, 31.161)
expert	6	30.2783	0.1765	(29.8129, 30.7437)

Pooled StDev = 0.549694

Calculated F test value = 23.83, P=0.000 which is< 0.05 level of significance. Ho is rejected. We conclude that average sales level at four different in-store locations are not same .

3) If you have seen evidence of difference among the average sales levels at these four different in-store locations, then identify which in-store locations have significantly different average sales than other in-store locations, by using the Tukey procedure.​

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 95% Confidence

Factor	N	Mean	Grouping
front	7	32.139	A
kiosk	8	30.758		B
expert	6	30.2783		B	C
Inasile	5	29.582			C

Means that do not share a letter are significantly different.

Tukey Simultaneous Tests for Differences of Means

Difference of Levels	Difference of Means	SE of Difference	95% CI	T-Value	Adjusted P-Value
front - Inasile	2.557	0.322	(1.662, 3.451)	7.94	0.000
kiosk - Inasile	1.175	0.313	(0.305, 2.046)	3.75	0.006
expert - Inasile	0.696	0.333	(-0.229, 1.621)	2.09	0.187
kiosk - front	-1.381	0.284	(-2.172, -0.590)	-4.85	0.000
expert - front	-1.860	0.306	(-2.710, -1.010)	-6.08	0.000
expert - kiosk	-0.479	0.297	(-1.304, 0.346)	-1.61	0.392

Individual confidence level = 98.91%

Tukey procedure shows front and Inasile are significant.

kiosk and Inasile are significant.

kiosk are front are significant.

expert and front are significant.