In R studio , create a dataset ( using `data.frame `) with two continuous variab

Question

In R studio, create a dataset (using `data.frame`) with two continuous variables of length 20, and one factor with 2 levels (a binomial variable), with 10 replicates each.

For the continuous variables, either enter them manually or use a random number generating a function that is appropriate to generate continuous variables.

Give the variables appropriate names and explain where the data set could have originated from / what experiment could have resulted in this data set.

5. Using the data set created in (4), test whether the two continuous variables are correlated. Include a null hypothesis, test for normality, use the appropriate test, and conclude, reporting the exact p-value.

Can someone please help me with this. Thank you.

Explanation / Answer

1. The code is given as follows:

#Creating the dataset
Height<-c(100,110,122,120,119,132,140,130,123,145,109,133,156,134,155,124,136,127,138,129)
Weight<-c(65,67,69,70,72,65,56,45,76,68,60,58,59,65,67,68,61,64,57,58)
Indicator<-c(0,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0)
dataset<-data.frame(Height,Weight,Indicator)
dataset

#Correlation Test
cor.test(Height,Weight,method = "pearson")

#Test for normality
shapiro.test(Height)
shapiro.test(Weight)

2. Explanation of the dataset:

The two continuous variables are Height and Weight of 20 employees in a company. The Indicator variable (the factor variable with 2 levels of 10 replicates each) is the indicator of them complying to a diet. 1 denotes the employee is on the diet and 0 denotes the employee is not on the diet.

All the variables are manually entered.

3. Test for correlation between the continuous variables:

Null Hypothesis: The variables are not correlated with each other vs Alternative Hypothesis: The variables are correlated with each other

Result:

Pearson's product-moment correlation

data: Height and Weight
t = -1.0872, df = 18, p-value = 0.2913
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
-0.6223890 0.2182587
sample estimates:
cor
-0.2482379

Interpretation: The p-value is greater than 0.05 and hence we may accept the null hypothesis and conclude that the variables are not correlated with each other.

4. Tests for normality:

We use the Shapiro Wilk Test for normality. This is the test generally used for testing normality of two continuous variables.

Null Hypothesis: The variable follows Normal population vs Alternative Hypothesis: The variable does not follow Normal population

Result:

Shapiro-Wilk normality test

data: Height

W = 0.98056, p-value = 0.9411

Shapiro-Wilk normality test

data: Weight

W = 0.95358, p-value = 0.4247

Interpretation: For both Height and Weight, the p-values are greater than 0.05 (level of significance) which implies that the we may accept the null hypotheses and conclude that both the variables come from or follow Normal distributions.

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