# Project #90410 - Stats and Propability

Suppose you are determining the association between the weight of a car and the miles per gallon that the car gets. Answer the following questions:

1.   In your own words, define correlation and talk about how you can use correlation to determine the relationship between these two variables.

2.   Before you look at some data, what kind of association do you think will exist between the weight of a car and the miles per gallon that the car gets? Will it be positive or negative?

3.   Given the data below, use Excel or other technology to calculate the correlation coefficient for this data:

 Model City MPG Weight Mazda MX-5 Miata 25 2365 Mercedes/Benz SLK 22 3020 Mitsubishi Eclipse 23 3235 Pontiac Firebird 18 3545 Porsche Boxster 19 2905 Saturn SC 27 2420

4.   Now that you have calculated the correlation, what does this value represent? What does it tell you about the relationship between these two variables?

Examples

Example 1: Safety experts are trying to determine how long it takes a specific brand of car to come to a complete stop. They have determined that the speed of the car has a large impact on how long it takes to come to a complete stop. They decide to gather data by having the car go 10, 30, 50, 70 and 90 miles per hour and then determine how many feet it takes to come to a complete stop at each of these speeds.

Example 2: Drama students at a large university recently put on a production of Phantom of the Opera. Some students jokingly said that only the female students went to see the play, and one of the students wanted to see if a higher proportion of female students had seen the play than males. To gather data, the student went around campus randomly selecting students and asking them their gender and if they went to see the production.

Complete the following for both Example 1 and Example 2:

5.   State the explanatory and response variables in each example, and state what type for each of the variables.

6.   For each example, discuss an appropriate analysis or procedure to use to determine if there is an association between the two variables.

7.   Given the following data where city MPG is the response variable and weight is the explanatory variable, explain why a regression line would be appropriate to analyze the relationship between these variables:

 Model City MPG Weight Mazda MX-5 Miata 25 2365 Mercedes/Benz SLK 22 3020 Mitsubishi Eclipse 23 3235 Pontiac Firebird 18 3545 Porsche Boxster 19 2905 Saturn SC 27 2420

8.   Construct the regression line for this data.

9.   Interpret the meaning of the y-intercept and the slope within this scenario.

10.                 What would you predict the city MPG to be for a car that weighs 3000 pounds?

11.                 If a car that weighs 3000 pounds actually gets 32 MPG, would this be unusual? Calculate the residual and talk about what that value represents.

 College Graduate Not a College Graduate Total Male 56 32 88 Female 62 41 103 Total 118 73 191

12.    Have the assumptions for this test been met? Why or why not?

13.    State the null and alternative hypothesis for this test.

14.    Calculate the test statistic for this test. Explain what this test statistic represents.

15.    Use technology, like Excel, to calculate the p-value for this test. Explain what this p-value represents.

16.    State the conclusion for this test at the 0.05 level of significance. Do you think these variables are dependent/associated? Why or why not?

17.    Describe the relationship between two variables that have a correlation coefficient value:

a.    Near -1

b.     Near 0

c.     Near 1

18.Data was collected where a weightlifter was asked to do as many repetitions as possible using different amounts of weight. Below is a table that shows how much weight was on the bar, and how many repetitions the weightlifter could do:

 Weight 200 300 400 500 Reps 42 27 12 3

a.    Calculate the correlation for this data. What does this value tell you about the relationship between these two variables?

b.    Determine the least squares regression line for this data. Interpret the values for the y-intercept and the slope within this scenario.

c.     Calculate r2 for this data and describe what it represents.

d.    Using the regression line from part (b), calculate the predicted number of repetitions for this weight lifter if the weight is 400 pounds, and then calculate and interpret the residual for that weight using the data.

19.Given the linear regression equation:

y = 1.6 + 3.5x1 – 7.9x2 + 2.0x3

a.    Which variable is the response variable? How many explanatory variables are there?

b.    If x1 = 2, x2 = 1 and x3 = 5, what is the predicted value for y?

c.     Supposed the n = 12 data points were used to construct the given regression equation above, and that the standard error for the coefficient x1 is 0.419. Construct a 90% confidence interval for the coefficient of x1.

d.    Using the information from part (c) and 5% level of significance, test the claim that the coefficient of x1 is different from 0. What does your conclusion mean in relation to x1 predicting y?

20.Suppose a researcher is analyzing the relationship between gender and favorite type of movie out of drama, science fiction and comedy. Here is the data using a random sample:

 Drama Science Fiction Comedy Total Male 28 152 218 398 Female 213 102 189 504 Total 241 254 407 902

Test whether gender and type of favorite movie are independent at the .05 level of significance. Show all five steps of this test.

21.Suppose you wanted to test whether M&M’s made the same amount of each color. You could run a goodness of fit test to see if each color had the same proportion. Suppose you took a sample of M&M’s and below is the breakdown by color:

 Color OBSERVED Counts Blue 15 Orange 14 Green 10 Yellow 11 Red 4 Brown 6 Total 60

Test whether each color has the same proportion. Show all five steps of this test at the 10% level of significance.

 Subject Mathematics Due By (Pacific Time) 11/01/2015 12:00 am
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