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Owner: c_boom416
Created: Dec 15, 2017
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Project Part 4
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1. Is your dataset a population or sample? Explain

     Yes it is. There are far more makes and models of cars than the ones present in my data set. 

a. One sample T hypothesis test:

μ : Mean of variable
H0 : μ = 24.760526
HA : μ ≠ 24.760526

Hypothesis test results:

VariableSample MeanStd. Err.DFT-StatP-value
MPG 24.760526 1.0621146 37 2.9732149e-7

1

            - variable(s) = MPG

           - null: mean =/= 24.76

           - alternative: mean = 24.76

           - statistic = T

           - Conclusion: due to the high p-value, the null hypothesis cannot be rejected

2. Set up and conduct a two-way table hypothesis test

Contingency table results:
Rows: MPG
Columns: Weight
  1.5 to 2 2 to 2.5 2.5 to 3 3 to 3.5 3.5 to 4 4 to 4.5 Total
15 to 20 0 0 0 3 7 2 12
20 to 25 0 0 5 2 0 0 7
25 to 30 0 2 6 0 0 0 8
30 to 35 3 5 1 0 0 0 9
35 to 40 1 1 0 0 0 0 2
Total 4 8 12 5 7 2 38

Chi-Square test:
StatisticDFValueP-value
Chi-square 20 58.648677 <0.0001
Warning: over 20% of cells have an expected count less than 5.
Chi-Square suspect.
 

           - variable(s) = MPG, Weight

           - null: MPG does not decrease with an increase in weight

           - alternative: MPG does decrease with an increase in weight

           - statistic = Chi-square

           - Conclusion: with a p-value of
 
3. Analysis of Variance results:
Data stored in separate columns.

Column statistics
ColumnnMeanStd. Dev.Std. Error
MPG 38 24.760526 6.5473138 1.0621146
Weight 38 2.8628947 0.70687041 0.11466952
Cylinders 38 5.3947368 1.6030288 0.26004561
Horsepower 38 101.73684 26.444929 4.289934

ANOVA table

SourceDFSSMSF-StatP-value
Columns 3 245519.54 81839.847 439.24881 <0.0001
Error 148 27575.026 186.31774    
Total 151 273094.57    

           - variable(s) = MPG, weight, cylinders, horsepower

           - null: many vehicles do not share similar characteristics in tersm of weight, power, and engine size

           - alternative: many vehicles do share similar characteristics in tersm of weight, power, and engine size

           - statistic = F

           - Conclusion: due to the low p-value of .0251, we can reject the null hypothesis at the .05 significance level. 




EC #1

One sample Z hypothesis test:

μ : Mean of variable
H0 : μ = 24.760526
HA : μ ≠ 24.760526
Standard deviation = 6.5473138

Hypothesis test results:

VariablenSample MeanStd. Err.Z-StatP-value
MPG 38 24.760526 1.0621145 2.9732149e-7 1

 all statistics, as well as the respective p-values, seem to be exactly the same. 

 

EC #4

I'm curious about the unit of measurment used in the cars' weights.  It is not given in the data set, and as the cars' years or manufacture are also not given, a google search yields different weights than are listed. While I'm not sure what other analysis would be appropriate, additonal variables like torue and drag coefficient would be helpful to include in the data set. 

Result 1: Frequency Table   [Info]
Frequency table results for MPG:
Count = 38
MPGFrequencyRelative FrequencyCumulative Frequency
15 to 20120.3157894712
20 to 2570.1842105319
25 to 3080.2105263227
30 to 3590.2368421136
35 to 4020.05263157938

HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=74638">Project Part 4</A>

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By xg15
Dec 16, 2017

In anova or hypothesis test, we are testing the population mean;
no conclusion for chisquare test;

Always Learning