- Given a sample mean of 14.2 and a sample standard deviation of 2.74
(with n=27), calculate the margin of error
(assume a 95% confidence interval will be generated).
Answer:
1.96 • 2.74 ÷ sqrt(27) = 1.03
- Given a sample mean of 14.2 and a sample standard deviation of 2.74
(with n=27), calculate the margin of error
(assume a 99% confidence interval will be generated).
The appropriate z-score is 2.576.
Answer:
2.576 • 2.74 ÷ sqrt(27) = 1.36
- A P-value is a way to express the confidence of our results.
For a one-tailed test,
it is the area under the curve to the right (or left) of our observed mean.
Calculate a z-score using our observed mean (14.2), expected mean (10.0),
and standard error (2.74/sqrt(27)) and sketch this region on a normal curve.
Answer:
(14.2 - 10.0)/(2.74 / sqrt(27)) = 7.96
- Alpha is the term used to express the level of significance we will
accept. For 95% confidence, alpha=0.05. If our P-value is less than alpha,
we can reject our null hypothesis (H0: µ=10).
Should we reject our null?
Answer:
YES!
- Do you think other coins might display similar characteristics?
How many times would you have to test it to reach a significant conclusion.
Answer:
That depends on how much the results differ from 50-50.
- How willing are you to bet money using this
method of "flipping" a coin
(assuming you have no scruples against such an activity)?
Answer:
$50? It does seem to be a fairly good bet!