STAT 3005 Lecture Notes - Lecture 6: Confidence Interval, Interval Estimation, Point Estimation

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26 Feb 2018

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Inference statistics allow us to make statements about a general population using the results of a random sample from the population. Point estimates are single values that would be used as a (cid:498)best guess(cid:499) for the parameter such as: (cid:1868) for (cid:1868),(cid:1877) for ,and (cid:1871) for . One must consider what is the probability that the answer is correct. This can be answered by assigning probabilities to intervals. Interval estimates are ranges of numbers in which the estimate is likely to fail. Confidence intervals are the most common interval estimate. They are computed from the sample data and can be thought as having a certain probability of containing the true parameter. Confidence level (c) is the probability of containing the true parameter value. It is written as (cid:883) and gives a (cid:4666)(cid:883) (cid:4667)(cid:883)(cid:882)(cid:882)% ci. Ci for proportion (cid:498)p(cid:499) are created by adding and subtracting the margin.

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Never forget that even small effects can be statistically significant if the samples are large. During a three-year period, 8 of the 57 headed by men and 6 of the 35 headed by women failed.

(a) Find the proportions of failures for businesses headed by women and businesses headed by men. These sample proportions are quite close to each other. Give the p-value for the hypothesis that the same proportion of women's and men's businesses fail. (Use two-sided alternative). What can we conclude (use alpha as 0.05)?

The p-value was ___________ so we conclude that ____________.

(b) Now suppose that the same sample proportion came from a sample 30 times as large. That is 180 out of 1050 businesses headed by women and 240 out of 1710 businesses headed by men fail. Verify that the proportions of failures are exactly the same as in part (a). Repeat the test for the new data. What can we conclude?

The p-value was ___________ so we conclude that ____________.

c) It is wise to use a confidence interval to estimate the size of an effect rather than just giving a p-value. Give 95% confidence intervals for the difference between proportions of men's and women's businesses that fail for the settings of both (a) and (b).

Interval for smaller samples: ___________ to ___________.

Interval for larger samples: ___________ to ___________.

What is the effect of larger samples on the confidence interval?

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Which of the following is NOT true when testing a claim about aproportion?

A. If you want to test a claim about population proportions, use the P-value method or the classical method of hypothesis testing.

B. When testing claims about population proportions, the traditional method and the P-value method are equivalent in the sense that they always yield the same result.

C. A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.

D. Both the traditional method and P-value method use the same standard deviation based on the claimed proportion p, but the confidence interval uses an estimated standard deviation based on the sample proportion ModifyingAbove p with caretp.

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STAT 3005 Lecture Notes - Lecture 6: Confidence Interval, Interval Estimation, Point Estimation

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Introductory Statistics

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