# Statistical Significance and Probablility

Your car gets 29 miles per gallon, one day you see your mileage average is 28 miles per gallon. Is this change statistically significantly and would you look for a reason or is it more of a variation attributed to chance?

Another day you see your mileage is 22 miles per gallon - Is this change statistically significantly and would you look for a reason or is it more of a variation attributed to chance?

How much of a decrease would you need to see before you thought it statistically significant?

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State the Null & Alternative Hypothesis for a test of significance:

A consumer group claims the amount of Iron in a health supplement capsule is less than the posted amount of 500 milligrams.

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P-Value & Dice: Use the table to test for bias against 6's, below shows probabliity of 6's in 100 tosses.

Number of 6's Probability

8 or fewer .006

10 or fewer .020

12 or fewer .052

In 100 tosses, 10 rolls are 6's. Is this result significant at the 0.05 level? What is the P-Value for this result?

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Thank you!

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#### Solution Preview

Please see response attached (also presented below) Good luck with your continued studies and take care.

RESPONSE:

Q1a: Your car gets 29 miles per gallon, one day you see your mileage average is 28 miles per gallon. Is this change statistically significantly and would you look for a reason or is it more of a variation attributed to chance?

A1a: We can use the range as a quick and easy indication of significance,

Range = plus or minus 6 (not significant)

In other words, when the mileage deviated any more than 6 miles per gallon either way, we would have a reason to consider the variation as significant. Thus, 28 miles per gallon, a variation on only 1 mile per hour, would more than likely be attributed to ...

#### Solution Summary

This solution provides solutions to three statistical questions concerning significance testing and probability.