A survey was recently conducted to determine if consumers spend more on computer

ID: 3156746 • Letter: A

Question

A survey was recently conducted to determine if consumers spend more on computer-related purchases via the Internet or store visits. Assume a sample of 8 respondents provided the following data on their computer-related purchases during a 30-day period. Using a .05 level of significance, can we conclude that consumers spend more on computer-related purchases by way of the Internet than by visiting stores?

Expenditures (dollars) Respondent In-Store Internet 1 132 225 2 90 24 3 119 95 4 16 55 5 85 13 6 248 105 7 64 57 8 49 0

Explanation / Answer

Given that n1 = 8 n2 = 8

(x-X)²

(y-Y)²

132

1000.1406

225

23485.5625

107.6406

2280.0625

119

346.8906

540.5625

7119.1406

280.5625

236.3906

3451.5625

248

21793.1406

105

1105.5625

1323.1406

217.5625

2639.3906

5148.0625

Total = 803

34565.8748

574

36509.5

X = 100.3750 Y = 71.7500

S2 = 1/n1+n2-2( (x-X)²+ (y-Y)²) =1/14 (34565.8748+36509.5)=362.6295

The null hypothesis is given by

H0 : µx = µy i.e., there is no significant difference between consumers purchasing via internet or store visit

Against the alternative hypothesis

H1 : µx > µy i.e., there is significant difference between consumers purchasing via internet or store visit is more

The test statistic is given by

t = X - Y/s2/(1/n1)+(1/n2) tn1+n2-2

t = 100.3750 – 71.7500/(362.6295)/(1/8)+(1/) t14

t = 28.6250/9.5214

tcal = 3.0064

the tabulated at 0.05 level of significance for right tailed test is 1.761 i.e., ttab = 1.761

here tcal > ttab so we reject the null hypothesis at 0.05 level of significance i.e., there is significant difference between consumers purchasing via internet or store visit is more