Question

Question 1:
The following bivariate data set contains an outlier.

x	y
51.7	82.9
51.3	75
52.5	71.4
52.5	74.2
43.6	66.6
37.1	81.8
52.8	63.4
58.4	59.8
61.7	49
35.9	79.9
62.7	76.6
43.4	69.3
35.5	86.9
50.6	57.3
144.3	200.6

What is the correlation coefficient with the outlier?
r_w =  

What is the correlation coefficient without the outlier?
r_wo =  

Would inclusion of the outlier change the evidence for or against a significant linear correlation at 5% significance? (Pick One)

No. Including the outlier does not change the evidence regarding a linear correlation.

Yes. Including the outlier changes the evidence regarding a linear correlation.

Would you always draw the same conclusion with the addition of an outlier? (Pick One)

Yes, any outlier would result in the same conclusion.
No, a different outlier in a different problem could lead to a different conclusion.

Explain your answer.

Question 2

A weight-loss program wants to test how well their program is working. The company selects a simple random sample of 62 individual that have been using their program for 18 months. For each individual person, the company records the individual's weight when they started the program 18 months ago as an x-value. The subject's current weight is recorded as a y-value. Therefore, a data point such as (185, 164) would be for a specific person and it would indicate that the individual started the program weighing 185 pounds and currently weighs 164 pounds. In other words, they lost 21 pounds.

When the company performed a regression analysis, they found a correlation coefficient of r = 0.762. This clearly shows there is a strong correlation, which got the company excited. However, when they showed their data to a statistics professor, the professor pointed out that correlation was not the right tool to show that their program was effective. Correlation will NOT show whether or not there is weight loss. Which tool would be more appropriate? (Pick One)

1-Sample Mean
2-Sample Mean (Matched Pairs)
1-Sample Proportion
2-Sample Mean (Independent Samples)
2-Sample Proportion
Explain what the correlation DOES show in this example, in terms of weights of individuals.

Question 3:
A weight-loss program wants to test how well their program is working. The company selects a simple random sample of 35 individual that have been using their program for 9 months. For each individual person, the company records the individual's weight when they started the program 9 months ago as an x-value. The subject's current weight is recorded as a y-value. Therefore, a data point such as (215, 194) would be for a specific person and it would indicate that the individual started the program weighing 215 pounds and currently weighs 194 pounds. In other words, they lost 21 pounds.

When the company performed a regression analysis, they found a correlation coefficient of r = 0.785. This clearly shows there is strong correlation, which got the company excited. However, when they showed their data to a statistics professor, the professor pointed out that correlation was not the right tool to show that their program was effective. Correlation will NOT show whether or not there is weight loss. Which tool would be more appropriate? (Pick One)

1-Sample Mean
2-Sample Mean (Matched Pairs)
1-Sample Proportion
2-Sample Mean (Independent Samples)
2-Sample Proportion
Explain what the correlation DOES show in this example, in terms of weights of individuals.

Answer 1

A)
What is the correlation coefficient with the outlier?
r_w =  

Pearson correlation of x and y = 0.843
P-Value = 0.000

B)

What is the correlation coefficient without the outlier?
r_wo =  

Pearson correlation of x and y = -0.579
P-Value = 0.030

C)
Would the inclusion of the outlier change the evidence for or against a significant linear correlation at 5% significance? (Pick One)

No. Including the outlier does not change the evidence regarding a linear correlation.

The p-value in both cases is less than 0.05.

D)

Would you always draw the same conclusion with the addition of an outlier? (Pick One)

Yes, any outlier would result in the same conclusion.

Outliers can change the direction of the correlation like positive correlation or negative correlation, but the conclusion will be the same which is a significant correlation.