Estimate and Interpret Population Variance
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With the data below can you tell me how I would estimate and interpret a population mean with the population standard deviation unknown.
Title Gross ($)
in Millions
Aliens 81.843
Armageddon 194.125
As Good As It Gets 147.54
Braveheart 75.6
Chasing Amy 12.006
Contact 100.853
Dante's Peak 67.155
Deep Impact 140.424
Executive Decision 68.75
Forrest Gump 329.691
Ghost 217.631
Gone with the Wind 198.571
Good Will Hunting 138.339
Grease 181.28
Halloween 47
Hard Rain 19.819
I Know What You Did Last Summer 72.219
Independence Day 306.124
Indiana Jones and the Last Crusade 197.171
Jaws 260
Men in Black 250.147
Multiplicity 20.1
Pulp Fiction 107.93
Raiders of the Lost Ark 242.374
Saving Private ryan 178.091
Schindler's List 96.067
Scream 103.001
Speed 2:Cruise Control 48.068
Terminator 36.9
The American President 65
The Fifth Element 63.54
The Game 48.265
The Man in the Iron Mask 56.876
Titanic 600.743
True Lies 146.261
Volcano 47.474.
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Solution Summary
The solution estimates and interprets a population variance. The solution uses Chi Square Distribution.
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We can estimate a variance with a point estimate and an interval estimate (a confidence interval). The point estimate for the population variance is the sample variance. The 95% interval estimate of the population variance is found using the formula below. If you want, you can also find a confidence interval for the population standard deviation by taking the square roots of the endpoints of the interval for the variance. I have shown this as well.
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