he following assignment will allow you to master the material on Correlation, Regression, Chi-Square and F Distributions and Nonparametric Statistics.
1. Explain in detail what is meant by correlation. (10 points)
a. Give three examples of a positive correlation and three examples of a negative correlation.
b. Describe at least one lurking variable for each of the correlations provided in part a.
c. Describe one outlier that could occur with each of your examples from part a.
2. You have been told that the amount of education a person obtains will guarantee them a high paying job. That is, their pay depends on their education. Discuss problems with this statement. Give a specific example of an individual that would be considered an outlier of this data set. (5 points)
3. You have been asked to find if there is a correlation between the amount of calories per serving in a bowl of cereal versus the amount of sugar (in grams) in the cereal. The following data has been given for examination.
Sugar Calories
18 200
23 210
12 170
12 190
37 220
19 175
23 201
22 210
32 210
11 190
11 197
29 205
a. Create a scatterplot of the given data. Be sure you explain your decision on which variable is the predictor and which variable is the response. (10 points)
b. Using computer software, calculate the correlation coefficient and interpret what this value implies in relation to the data set. (5 points)
c. Create a regression equation that models the data and describe the values of the slope and y-intercept with the data set. (5 points)
d. Predict if a box of cereal has 25 grams of sugar per serving how many calories it will contain. (5 points)
e. Predict if a box of cereal has 230 calories per serving how much sugar (in grams) it will contain. (5 points)
f. Discuss any lurking variables could be relevant to analysis of this data set. (5 points)
4. A market analysis wishes to see whether consumers have any preference between five different flavors of chewing gum. A sample of 100 people provided the data below. Does enough evidence exist to reject the claim that no preference exists in the selection of chewing gum flavors? (10 points)
Frequency Observed Expected
Mint 32 20
Bubble Gum 28 20
Strawberry 16 20
Grape 14 20
Orange 10 20
5. A medical researcher wishes to see whether the variance of the heart rates (in beats per minute) of smokers is different from the variance of heart rates of people who do not smoke. Below is the data from two samples. Using α = 0.05, is there enough evidence to support the claim? (10 points)
Smokers Non-Smokers
n1 = 26 n2= 18
s12 = 32 s22 = 10
6. Discuss in general the use of the Sign Test for Matched Pairs, Rank-Sum Test and the Spearman Rank Correlation Test. (10 points)
Please complete all components of this assignment in a single Microsoft Word document and then upload your document to be graded using the dropbox below.
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