Question

Using your preferred technology format (StatCrunch, Statdisk, Excel), generate a scatterplot for these two data sets. Based on the graph, do you believe the two sets are correlated?

Now, complete a hypothesis test to test the claim that the course rating and the professor rating are correlated. Explain your conclusion in statistical and non-statistical terms and how you arrived at that conclusion. You should include your null and alternative hypothesis (in English and in symbolic form), your significance level, whether you are conducting a right tailed, left tailed, or two tailed test, r-value, p-value, and conclusions.

COURSE EVAL   PROF EVAL
4.3   4.7
4.5   4.6
3.7   4.1
4.3   4.5
4.4   4.8
4.2   4.4
4   4.4
3.4   3.4
4.7   4.8
3.9   4
3.1   3.6
4   4.1
3.8   4.1
3.4   3.5
2.9   2.9
4.5   4.6
4   4.4
3.8   4
4.3   4.9
3.4   3.5
3.4   3.7
3.3   3.4
4.3   4.3
4.4   4.5
4.1   4.3
4.6   4.8
4.2   4.4
4   4.4
3.3   3.6
4.4   4.6
2.3   2.3
3.5   4.3
4.7   4.9
3.9   4.2
4   4.2
4.3   4.3
3.8   3.9
3.8   3.9
4   4.1
4.6   4.8
3.5   3.3
4.7   4.4
3.4   3.3
3.9   4
4.5   4.5
4.7   4.9
3.5   3.7
3.7   3.9
4   4.4
4.1   4.4
4.4   4.5
4.2   4.3
4.5   4.8
3.8   4.1
3.1   3.5
3.7   4
3.9   3.8
4   4.1
3.3   3.7
3.1   3.2
4   4.2
4.3   4.5
3.7   3.8
3.4   3.7
4.3   4.5
3.7   3.8
4.2   4.5
2.2   2.4
3   3
4.3   4.5
3.5   3.5
4.6   4.8
3.7   4.2
3.8   4
3.6   3.7
4.4   4.5
4.1   4.7
4.3   4.3
4   4
4.8   4.9
3.5   3.5
3.6   3.3
3.8   4.2
4.7   4.8
4.9   4.9
4.3   4.5
3.3   3.3
3.4   3.3
3.6   3.6
4   4.1
3.9   3.7
4.3   4.5
3.3   3.5

Answer 1

Sol:

used R technolgy

create a table course

use cor.test function to get the hypothesis test for correlation

plot function to get the scatteplort in R

Rcode:

course =read.table(header = TRUE, text ="
COURSEEVAL PROFEVAL
4.3 4.7
4.5 4.6
3.7 4.1
4.3 4.5
4.4 4.8
4.2 4.4
4 4.4
3.4 3.4
4.7 4.8
3.9 4
3.1 3.6
4 4.1
3.8 4.1
3.4 3.5
2.9 2.9
4.5 4.6
4 4.4
3.8 4
4.3 4.9
3.4 3.5
3.4 3.7
3.3 3.4
4.3 4.3
4.4 4.5
4.1 4.3
4.6 4.8
4.2 4.4
4 4.4
3.3 3.6
4.4 4.6
2.3 2.3
3.5 4.3
4.7 4.9
3.9 4.2
4 4.2
4.3 4.3
3.8 3.9
3.8 3.9
4 4.1
4.6 4.8
3.5 3.3
4.7 4.4
3.4 3.3
3.9 4
4.5 4.5
4.7 4.9
3.5 3.7
3.7 3.9
4 4.4
4.1 4.4
4.4 4.5
4.2 4.3
4.5 4.8
3.8 4.1
3.1 3.5
3.7 4
3.9 3.8
4 4.1
3.3 3.7
3.1 3.2
4 4.2
4.3 4.5
3.7 3.8
3.4 3.7
4.3 4.5
3.7 3.8
4.2 4.5
2.2 2.4
3 3
4.3 4.5
3.5 3.5
4.6 4.8
3.7 4.2
3.8 4
3.6 3.7
4.4 4.5
4.1 4.7
4.3 4.3
4 4
4.8 4.9
3.5 3.5
3.6 3.3
3.8 4.2
4.7 4.8
4.9 4.9
4.3 4.5
3.3 3.3
3.4 3.3
3.6 3.6
4 4.1
3.9 3.7
4.3 4.5
3.3 3.5
"
)
df1

plot(PROFEVAL~COURSEEVAL,pch=16,data=course,xlab = "COURSEEVAL",
ylab = "PROFEVAL",main="Scatter Plot",col="green")
cor.test(course$COURSEEVAL,course$PROFEVAL)

Output:

Pearson's product-moment correlation

data: x and y
t = 27.246, df = 91, p-value < 2.2e-16
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.9162851 0.9624811
sample estimates:
cor
0.943824

Intrepretation:

Form scatterplot the points are clustered

Form:linear

strength:strong

Direction:positive

r=0.9438

Hypothesis test for correlation

Ho:

course rating and the professor rating are not correlated.

Ha:

course rating and the professor rating are correlated.

Its a two tailed test

alpha=0.,05

r=0.943824

n=91

t= 27.246

p-value < 2.2e-16

p value=0.0000

p<0.05

Reject Ho

Accept Ha

Conclusion:There is suffcient statistical evidence at 5% level of significance to conlcude that course rating and the professor rating are correlated.

There exists a strong positve relationship bewteen course rating and professor rating and relationship is statistically significant.