Describe the assumptions needed for Question 1.] [State whether these assumption

Question

Describe the assumptions needed for Question 1.]

[State whether these assumptions for Question 1 are met. If there is no way to know, you should mention that.]

Then repeat the above for Questions 2-6.

Data: https://1drv.ms/f/s!AjoNcITDywDK3HLWgpXzOLgH7UWV

Questions of Interest. Here are the questions that you should address in this data analysis. For each question below, you should answer the question as specifically as you can Question 1. What are the true average plasma retinol and (log) plasma beta-carotene levels in the population? Question 2. ls there a difference in plasma retinol level between males and females? Question 3. Is there a relationship between grams of fat and grams of fiber consumed per day? Question 4. Is there a relationship between smoking status and gender? Question 5. Is vitamin use in the population the same across all categories? (Vitamin Use cate- gories: Yes, fairly often; Yes, not often; and No) Question 6. Does plasmal retinol level differ across different smoking statuses? (Smoking Status categories: Never, Former, and Current Smoker)

Explanation / Answer

data1=read.table(file.choose(),header=T) #reading the data plasma.txt
attach(data1)

1. Assumption : sample mean is truly representative of the population mean.

mean(Retplasma)
Average Plasma Retinol = 602.7905

mean(Betaplasma)
Average (log) Beta-Carotene level = 189.8921

2. femret=Retplasma[Sex==2] # subsetting the plasma retinol levels for females
maleret=Retplasma[Sex==1] # subsetting the plasma retinol levels for males

#t-test for testing if there is a difference in retinol levels for males and females
t.test(femret,maleret,alt="two.sided",mu=0,paired=FALSE,var.equal = FALSE,conf.level=0.95,)

Welch Two Sample t-test

data: femret and maleret
t = -2.3157, df = 45.685, p-value = 0.02512
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-211.27180 -14.76117
sample estimates:
mean of x mean of y
587.7216 700.7381

Since p-value < 0.05, we reject the null hypothesis and conclude that there is a difference in retinol levels for males and females.

3.

#correlation-test for testing if there is a relationship between grams of fat and gram of fiber consumed per day
cor.test(Fat,Fiber)

Pearson's product-moment correlation

data: Fat and Fiber
t = 5.0899, df = 313, p-value = 6.193e-07
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.1712066 0.3755181
sample estimates:
cor
0.2764836

Since p-value is very small, we reject the null hypothesis and conclude that there is a relationship between the grams of fat and grams of fiber consumed per day.

4.

#correlation-test for testing if there is a relationship between smoking status and gender
cor.test(Smokstat,Sex)

Pearson's product-moment correlation

data: Smokstat and Sex
t = -2.1571, df = 313, p-value = 0.03176
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
-0.22848125 -0.01066385
sample estimates:
cor
-0.1210292

Since p-value < 0.05, we reject the null hypothesis and conclude that there is a relationship between the smoking status and gender.

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