In this week\'s data analysis, we will explore the cereal dataset. This dataset

Question

In this week's data analysis, we will explore the cereal dataset. This dataset consists of the sodium content (mg) of various cereal brands by the manufacturers Kellogg's and General Mills. Please look at R Guide Week 4 for an example of how to do many of the tasks below. (a) Download the file cereal.txt from Canvas and load it into R. This will again involve setting your Working Directory. See R Guide Week 2 (or alternatively the announcement on Canvas if you are using R Studio) for a reminder on how to do this. Use the head() and print() commands to view the first six observations and the entire dataset, respectively. Report the sodium content of the 4^th and 16^th observations. (b) Construct a 90% confidence interval for the average sodium content of all cereals made by these two manufacturers. Interpret this confidence interval. (c) Find the standard deviation of sodium content for each manufacturer in our data. Use this information to very that we should use the pooled variance scenario. (d) Conduct a pooled variance 2 sample t test to assess whether cereals produced by General Mills have a higher sodium content on average than cereals produced by Kellogg's. Write down the hypotheses, and state the p-value and your conclusion. Use alpaha = 0.05.

Explanation / Answer

#b-to calculate confidence interval

me=mean(mydata$Sodium) #mean of Sodium

std_dev=sd(mydata$Sodium) #standard deviation of Sodium

error=qt(0.95,df=length(mydata$Sodium)-1)*sd(mydata$Sodium)/sqrt(length(mydata$Sodium))

#c

manf1_sodium_content=mydata[mydata$Manufacturer=="K","Sodium"] #"General Mills" Sodium data

manf2_sodium_content=mydata[mydata$Manufacturer=="G","Sodium"] #"Kellogg's" Sodium data

std_manf_K=sd(manf1_sodium_content) #standard deviation of Sodium corresponding to "General Mills"

std_manf_G=sd(manf2_sodium_content) #standard deviation of Sodium corresponding to "Kellogg's"

#d

t_test=t.test(manf1_sodium_content,manf2_sodium_content,alternative="greater",var.equal=TRUE,conf.level=0.95)

#Hypothesis

#H0:mu1=mu2 Vs H1:mu1>mu2 where mu1:mean of Sodium corresponding to "General Mills" & mu2=mean  of Sodium corresponding to "Kellogg's"

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