1) What are Type I and Type II errors? 2) Why do we use pˆ (p-hat)...

1) What are Type I and Type II errors?

2) Why do we use pˆ (p-hat) in place of p when doing confidence intervals but use p0 (‘p naught’) in

place of p when doing hypothesis tests?

3) What are the two criteria used to choose the best estimator for a population parameter?

4) Suppose you have calculated a confidence interval for a single mean with alpha equal to 0.05, and the

interval ranges from 5 and 10. Describe in a single sentence what the confidence interval is indicating.

5) Why is it safe to approximate the proportion p (or pˆ if you prefer) with 0.5 when calculating the

necessary sample size to achieve a desired confidence interval width?

Homework Answers

Answer #1


Type 1 error is probability of rejecting a true null hypothesis .

Type 2 error is probability of acceptance of a false null hypothesis.


p_hat is used to show the estimated value of p.

p is the actual value . p is unknown ,so we estimate the value of p and denote it by p_hat.

p0 is the given value of p to be compared with.

Clearly, p is the population proportion

p_hat is sampple proportion.



Consistency and Efficiency

These are the criteria.


Population mean lies between 0 to 5


For p=.5 , conservative margin of error will be okay.

If p far from .5 resulting interval will be be wider than needed.

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