Part 4: Complete this part AFTER you have generated all 20 of the confidence int
ID: 3255517 • Letter: P
Question
Part 4: Complete this part AFTER you have generated all 20 of the confidence intervals.
(a) How many of the 20 different 80% confidence intervals actually contained the true value of p? How did that compare to your answer from Part 2(d)
Part 2(d)= 16
(b) People who do not understand the theory behind confidence intervals will often interpret them incorrectly. Once an 80% confidence interval is constructed, some people will say, “There is a probability of 0.80 that the confidence interval contains the true value of p.” Explain why this interpretation is VERY WRONG.
Explanation / Answer
(a)
The 20 different confidence intervals
An 80% confidence interval means that if we repeat the same experiment under the same circumstances and same sample size many times, then 80% of these sample confidence intervals would contain the population parameter.
So, if we are taking 20 such samples, then 80% of these intervals would include the actual value of 'p', which is -
20 x 0.8 = 16
So, 16 such samples would contain the actual/true value of 'p'.
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b)
This interpretation is very wrong because -
A 95% confidence interval does not mean that for a given interval there is a 95% probability that the population parameter lies within the interval.
Once an experiment is done and an interval calculated, this interval either covers the parameter value or it does not; it is no longer a matter of probability. The 95% probability relates to the reliability of the estimation procedure, not to a specific calculated interval.