STAT200 Lecture Notes - Lecture 7: Confidence Interval, Central Limit Theorem, Interval Estimation

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violetmuskrat44

4 Aug 2018

School

University of Delaware

Department

Statistics

Course

STAT200

Professor

Ilvento Thomas

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Document Summary

Confidence intervals for large sample means: confidence intervals, remember, we only have one sample, and this one interval estimate. If o- is known, use z-value for the c. i. similar to proportions. If o- is unknown, and the sample size is sufficiently large, you can use s to estimate o- and a z-value for the c. i. If the sample size is small (<30) and the distribution is appox. Normal, use the t-distribution with n-1 degrees of freedom. Confidence intervals for small sample means: an estimator- either the sample proportion or the mean, confidence interval for a mean. I have two estimates: the estimate of the mean, the estimate of the sd which i used to estimate the se. Issues of normality and sample size when using s. Is it a problem to use the sample estimate of s when o- is not known.

Related Questions

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?

viridiancoyote964

6. As the test statistic becomes larger, the p-value

(a) gets smaller

(b) becomes larger

(d) becomes negative.

7. To describe the sampling distribution of the sample proportion, we use

(a) The sample proportion

(b) The population proportion

(d) The population mean

8. When small samples are used to estimate a population mean, in cases where the population standard deviation is unknown and the original distribution is normal:

(a) There always will be a large amount of sampling error.

(b) the t-distribution must be used to obtain the critical value.

(d) the z distribution must be used to obtain the critical value.

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STAT200 Lecture Notes - Lecture 7: Confidence Interval, Central Limit Theorem, Interval Estimation

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