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1 answer below »
I don't have the PDF or word version of it but I will do my best to provide it


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Answered Same DayJun 12, 2021

Answer To: "","group","prev","post" "1","A","194.6","302.3" "2","A","330.08","0" "3","A","331.16","67.6"...

Pooja answered on Jun 13 2021
153 Votes
**group**: "A" if the user was in the control group, "B" if the user was in the treatment group and hence had their background color changed to cream.
**prev**: numeric variable representing the amount the user spent on Amazon in the month prior to the (poss
ible) color change.
**post**: numeric variable representing the amount the user spent on Amazon in the month after the color change went into effect for group "B".
You are of course welcome/encouraged to do a preliminary exploration of this data, but this exploration should not be included in your submission (unless relevant to answering one of the questions).
---
##Problem \# 1: A/B testing
Complete the following A/B tests, including computation and interpretation of a p-value. Show your work, including any R code used.
a. Test the difference in means (between group $A$ and group $B$) for the "post" variable.
> t.test(post~group,data=data1)
    Welch Two Sample t-test
data: post by group
t = 0.4874, df = 14672, p-value = 0.626
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-4.080028 6.780636
sample estimates:
mean in group A mean in group B
119.6497 118.2994
With t=0.4874, p>5%, I fail to reject null hypothesis and conclude that there is no significant difference in the post between group $A$ and group $B$.
b. Test the difference in proportions (between group $A$ and group $B$) of users that increased their spending from prev to post.
> diff <- c(data1$post-data1$prev)
> data1$diff <- c(data1$post-data1$prev)
> View(data1)
> data1$increase <- ifelse(data1$diff>0, 1, 0)
> addmargins(table1)

A B Sum
0 5872 6795 12667
1 1128 1205 2333
Sum 7000 8000 15000
> prop.test(x = c(1128, 1205), n = c(7000, 8000))
    2-sample test for equality of proportions with continuity correction
data: c(1128, 1205) out of c(7000, 8000)
X-squared = 3.0649, df = 1, p-value = 0.08
alternative hypothesis: two.sided
95 percent confidence interval:
-0.001261453 0.022297167
sample estimates:
prop 1 prop 2
0.1611429 0.1506250
With z=.0639, p>5%, I fail to reject the null hypothesis at 5% level of significance and conclude that there is no significant difference in the proportion between group $A$ and group $B$) of users that increased their spending from prev to post.
## Problem \#2: Linear Regression
a. Find the equation for the linear regression of the `post` variable predicted from both the `prev` model and a boolean indicator for whether the person had their background...
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