Question

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?

Answer #1

1)

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

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

2)

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.

p_{0} is the given value of p to be compared with.

Clearly, p is the population proportion

p_hat is sampple proportion.

3)

Unbiasedness

Consistency and Efficiency

These are the criteria.

4)

Population mean lies between 0 to 5

5)

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

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

1) Explain what inferential statistics is used for
2) Define briefly and in your words the p-value
3) Provide an example where a hypothesis test would be worth
doing with a null hypothesis μ1-μ2 = 0, and with an alternative
hypothesis of μ1-μ2 ≠ 0
4) Explain why, in confidence intervals, when moving from a case
in which the population variance is known to another in which this
value is estimated from samples (sample variance), the length of
the interval...

1.The sample mean is an unbiased estimator for
the population mean. This means:
The sample mean always equals the population mean.
The average sample mean, over all possible samples, equals the
population mean.
The sample mean will only vary a little from the population
mean.
The sample mean has a normal distribution.
2.Which of the following statements is
CORRECTabout the sampling distribution of the
sample mean:
The standard error of the sample mean will decrease as the
sample size increases....

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