Question

A firm wanted to know if the cost of acquiring a new customer had decreased after adopting a new marketing campaign. Which statistical test should you run? A.Independent-samples t-test B.ANOVA C.One-sample t-test D.Paired-samples t-test

Before or After	customer cost
before	$             15.04
before	$             20.41
before	$              8.84
before	$             17.54
before	$              7.30
before	$             12.69
before	$             13.32
before	$             10.51
before	$             15.85
before	$             12.15
before	$             12.64
before	$              6.75
before	$             13.57
before	$             10.17
before	$             22.91
before	$             18.48
before	$             15.06
before	$             11.23
before	$              8.38
before	$             12.80
before	$             19.57
before	$              7.88
before	$              8.43
before	$              7.13
before	$             13.42
before	$             10.03
before	$             16.10
before	$             14.17
before	$              8.06
before	$             11.28
after	$             20.14
after	$             14.85
after	$             24.50
after	$             23.68
after	$             16.28
after	$             23.10
after	$             20.74
after	$              9.81
after	$              7.04
after	$             27.26
after	$             14.64
after	$             16.93
after	$             24.40
after	$             19.66
after	$             25.29
after	$             27.99
after	$             25.70
after	$             19.48
after	$             23.06
after	$             21.43
after	$             17.74
after	$             21.43
after	$             18.01
after	$             19.19
after	$             17.05
after	$             15.36
after	$             13.19
after	$             31.47
after	$             21.00
after	$              4.72

Answer 1

Which statistical test should you run?

Ans: here we use Paired-samples t-test because sample observation for customer cost is Before and  After are dependent in pairs

# Paired-samples t-test is used hence option D is correct

> x=scan("clipboard");x
Read 30 items
[1] 15.04 20.41 8.84 17.54 7.30 12.69 13.32 10.51 15.85 12.15 12.64 6.75
[13] 13.57 10.17 22.91 18.48 15.06 11.23 8.38 12.80 19.57 7.88 8.43 7.13
[25] 13.42 10.03 16.10 14.17 8.06 11.28> y=scan("clipboard");y

Read 30 items
[1] 20.14 14.85 24.50 23.68 16.28 23.10 20.74 9.81 7.04 27.26 14.64 16.93
[13] 24.40 19.66 25.29 27.99 25.70 19.48 23.06 21.43 17.74 21.43 18.01 19.19
[25] 17.05 15.36 13.19 31.47 21.00 4.72
> #x= cost of customer before adopting a new marketing campaign.
> #y=cost of customer after adopting a new marketing campaign.
> #di=yi-xi
> #Ho:average cost of customer before and after adopting a new marketing campaign are same
> #ieUd=0
> #Ha:average cost of customer before is decrease after adopting a new marketing campaign

ie Ud<0
> t.test(y,x,paired=T,alternative="l")

Paired t-test

data: y and x
t = 5.3896, df = 29, p-value = 1
alternative hypothesis: true difference in means is less than 0
95 percent confidence interval:
-Inf 8.918798
sample estimates:
mean of the differences
6.781
# hence p-value=1 is grater than 0.05 hence we accept H0 at 5% level o significance

Conclusion:hence accept Ho and conclude that cost of customer before and after adopting a new marketing campaign are same