Question

Front of the store Aisle of the store

224 192

189 236

248 164

285 154

273 189

190 220

243 261

215 186

280 219

317 202

Consider a company that stocks it's CD players in stores. It wants to determine if the location on where their product is placed in the store matters for sales generated. They contract with the retailer to place their product in the “front of the store” or in the “aisle of the store.” The collected data on the sales of their products separated by the location in the store. Test whether there is a significant difference in the mean sales across the two different locations in the store.

Using software:

a. Generate summary statistics (central tendency and variability measures) for the two samples and briefly summarize what they say.

b. Construct a 95% confidence interval of the difference between the two population mean delivery times and interpret it.

c. Finally, are there any other factors, besides the way the store is classified, that could possibly influence delivery times (identify at least 2)? Include a brief explanation of each.

Answer 1

(a) let x=front of the store, y=aisle of the store

x=c(224,189,248,285,273,190,243,215,280,317)
summary(x)

output : Min. 1st Qu. Median Mean 3rd Qu. Max.
189.0 217.2 245.5 246.4 278.2 317.0

y=c(192,236,164,154,189,220,261,186,219,202)
summary(y)

output : Min. 1st Qu. Median Mean 3rd Qu. Max.
154.0 186.8 197.0 202.3 219.8 261.0

(b) 95% C.I. of the difference between the two population mean

Answer: Here, we use the t-test because the sample size is small(<30).

R-code: x=c(224,189,248,285,273,190,243,215,280,317)
y=c(192,236,164,154,189,220,261,186,219,202)

t.test(x,y)

output:

Welch Two Sample t-test

data: x and y
t = 2.6041, df = 16.843, p-value = 0.01862
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
8.345485 79.854515
sample estimates:
mean of x mean of y
246.4 202.3

95% confidence interval=(8.345485 , 79.854515)