Question 1. Online shopping statistics are routinely reported by www.shop.org. Of interest to many online retailers are gender-based differences in shopping preferences and behaviours. The summary data of monthly online expenditures for a sample of male and female online shoppers are shown in the following table:
Male | Female | |
n | 45 | 45 |
Mean | $352 | $310 |
StDev s | $95 | $80 |
Find the 90% confidence interval for the difference in mean monthly online expenditures between males and females.
lower bound of confidence interval (use 2 decimal
places in your answer).
upper bound of confidence interval (use 2 decimal
places in your answer).
Question 2
In the answer boxes below the table, provide the values for the table cells that have question marks.
xbar | s_{x} | ybar | s_{y} | r | intercept of least sq. line | slope of least sq. line | |
a) | 30 | 4 | 18 | 6 | -0.2 | ?? | ?? |
b) | 100 | 18 | 60 | 10 | 0.9 | ?? | ?? |
c) | ?? | 0.8 | 50 | 15 | ?? | -10 | 15 |
d) | ?? | ?? | 18 | 4 | -0.6 | 30 | -2 |
Row a).
intercept
slope
Row b).
intercept
slope
Row c).
xbar
r
Row d).
xbar
s_{x}
ANs 1 ) using minitba>stat>basic stat>two sample t
we have
Two-Sample T-Test and CI
SE
Sample N Mean StDev Mean
1 45 352.0 95.0 14
2 45 310.0 80.0 12
Difference = μ (1) - μ (2)
Estimate for difference: 42.0
90% CI for difference: (11.2, 72.8)
T-Test of difference = 0 (vs ≠): T-Value = 2.27 P-Value = 0.026 DF
= 88
Both use Pooled StDev = 87.8208
lower bound of confidence interval =11.20
upper bound of confidence interval =72.8
Ans 2 )slope = r*sx/sy , intercept= y bar- slope*xbar
xbar | sx | ybar | sy | r | intercept of least sq. line | slope of least sq. line | |
a) | 30 | 4 | 18 | 6 | -0.2 | intercept = 18-(-0.3)*30= 27 | slope = -0.2*6/4 = -0.3 |
b) | 100 | 18 | 60 | 10 | 0.9 | intercept = 60-(0.5)*100= 10 | slope = 0.9*10/18 =0.5 |
c) | =(50-(-10))/15= 4 | 0.8 | 50 | 15 | r= 15*0.8/15 =0.8 | -10 | 15 |
d) | = (18-30)/-2= 6 | =-0.6*4/-2 = 1.2 | 18 | 4 | -0.6 | 30 | -2 |
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