Homework Assignment 4
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Pikes Peak Community College *
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MISC
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
docx
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Homework Assignment 4
Q1. A shop that makes smoothy drinks uses a recipe for its banana smoothy drinks in which the drink is
supposed to contain 10 grams of sugar. The drinks are produced by a special machine that adds the sugar
in a container before it mixes everything. An employee is suspicious that the machine does not add 10
grams of sugar for each drink. If proven right, the machine must be replaced. You store the level of sugar
of 25 drinks in a variable called Drink sugar.
Drink sugar
[1]
9.976959 10.012098
9.963002
9.998574 10.002431 10.036959
[7] 10.014752
9.985491 10.026681
9.981070 10.011058
9.958206
[13] 10.047110
9.931327
9.980533
9.982266
9.956010
9.992339
[19]
9.957293
9.907988
9.983450 10.018341
9.979281
9.931443
[25] 10.019777
You must do a test that can address employee concerns, i.e., the test is to tell you if the level of sugar is
different from the approved recipe.
a)
Write the null (H0) and alternative hypothesis (H1)
b)
What type of t-test is the most appropriate?
c)
Write a script to perform the suggest test in b and report the results of analysis, do you reject or
accept the null hypothesis, why, and what does this means?
Q2. A chain of membership-only retail warehouse clubs is interested in knowing the impact of a discount
program on the sales. To investigate the impact, the company decided to follow the daily sales of one of
its shops. The management wants to know if there is a statistical difference between the average sales of
the shop before and after the program. The company provides the daily tracked sales of the branch from
7 days before the discount program started in the branch (Daily_Sale_Before_Discount_Program) and for
the 7 days during which the discount program been promoted (Daily_Sale_After_Discount_Program) to
statistician.
a)
What type of t-test do you perform to answer the management concerns about the discount
program? why?
b)
What is the null and alternative hypothesis?
c)
Write an R script to perform the test
d)
What is the outcome of the test and what is your report/recommendation to management based
on your statistical analysis?
> Daily_Sale_Before_Discount_Program
[1] 49971.98 49988.49 50077.94 50003.53 50006.46 50085.75 50023.05
> Daily_Sale_After_Discount_Program
[1] 50011.75 50040.66 50052.72 50136.20 50092.99 50095.04 50080.53
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