. A study concerning auto speeds and fuel consumption rates, measured in miles p
ID: 3175185 • Letter: #
Question
. A study concerning auto speeds and fuel consumption rates, measured in miles per gallon, produced the following data.
Speed
Fuel Consumption (miles per gallon)
44
22
51
26
48
21
60
28
66
33
61
32
Compute the sample correlation coefficient. You may use the statistical formulas for the sample mean and standard deviation in Excel, but you must show your calculation for the sample correlation coefficient in the space below.
Suppose we want to test, at the 0.05 significance level, if there is positive correlation between speed and MPG in the population.
State the null and alternative hypothesis:
What is the critical value(s) of the test statistic?
State the decision rule:
Compute the value of the test statistic:
What is your conclusion?
Determine and interpret the p-value.
Compute the value for the estimated y-intercept and slope, and write out the estimated regression equation.
Speed
Fuel Consumption (miles per gallon)
44
22
51
26
48
21
60
28
66
33
61
32
Explanation / Answer
Step 1: Find XY , X2 and Y2 as it was done in the table below.
Step 2: Find the sum of every column to get:
X=330 , Y=162 , XY=9112 , X2=18518 , Y2=4498
Step 3: Use the following formula to work out the correlation coefficient.
r =sqrt( nXYXY/[nX2(X)2][nY2(Y)2])= sqrt(69112330162/[6185183302][644981622])0.9456
X Y XY XX YY 44 22 968 1936 484 51 26 1326 2601 676 48 21 1008 2304 441 60 28 1680 3600 784 66 33 2178 4356 1089 61 32 1952 3721 1024Related Questions
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