Question

A calculus instructor is interested in finding the strength of a relationship between the final exam grades of students enrolled in Calculus I and Calculus II at his college. The data (in percentages) are listed below. Complete the hypothesis test to predict the Calculus II grade if the Calculus I grade was 80?

Calculus 1: 88 78 62 75 95 91 83 86 98

Calculus 2: 81 80 55 78 90 90 81 80 100

1. By visual observation of the scatter plot, does the data appear linear?

2. Null Hypothesis:

3. Alternative Hypothesis:

4. What is the p-value?

5. Is there sufficient evidence to support a claim of a linear correlation between the two variables? Why or why not? Explain why you rejected or failed to reject the null.

6. If there is a correlation, what is the regression equation?

7. What is the best prediction of the Calculus II grade if the Calculus I grade was 80?

Answer 1

Ans:

Yes,appear linear.

	calculus I	calculus II
1	88	81
2	78	80
3	62	55
4	75	78
5	95	90
6	91	90
7	83	81
8	86	80
9	98	100
mean	84	81.667
SD	11.113	12.278
r	0.945
slope	1.044
intercept	-5.989

Correlation coefficient,r=0.945

n=9

Test statistic:

t=0.945*sqrt((9-2)/(1-0.945^2))

t=7.64

df=9-2=7

p-value=tdist(7.64,7,2)=0.0001

Reject the null hypothesis.

There is sufficient evidence to support a claim of a linear correlation between the two variables.

Regression equation:

y'=1.044x-5.989

when class I grade is 80

Class II predicted grade:

y'=1.044*80-5.989=77.53