STAT150 Lecture Notes - Lecture 5: Confidence Interval, Interval Estimation, Binomial Distribution

175 views2 pages

orchidgiraffe317

29 Jun 2018

School

Department

Course

Professor

For unlimited access to Class Notes, a Class+ subscription is required.

STAT150 LECTURE – 28/3/18

WK5: PROPORTIONS

Sampling Distributions for Proportions Confidence Intervals for Population Proportions

SAMPLING DISTRIBUTIONS FOR PROPORTIONS

- When np and nq are at least 10, the normal distribution can be used to approximate

the Binomial distribution.

- We use the sample proportion, p^, as an estimate of the population proportion, p.

- A sample statistic is something we can calculate from a sample

- We can take lots of samples and we will obtain different sample statistics that vary

- A sampling distribution is the distribution of sample statistics

- The sampling distribution shows us how much sample statistics vary from sample to

sample

CONFIDENCE INTERVAL FOR ESTIMATING A POPULATION PROPORTION, P

- We use sample statistics to estimate population parameters

- When we take a sample from a population and calculate a statistic (or point

estimate) we are trying to estimate a population parameter

oWe use the point estimate p^ to estimate p

- Often it is more informative to give an interval estimate for the parameter, rather

than a point estimate

- Due to the variance in sample proportions an interval estimate is more beneficial as

it gives us a range of believable values for the parameter

- We call the interval/range of believable values a confidence interval

find more resources at oneclass.com

Unlock document

This preview shows half of the first page of the document.
Unlock all 2 pages and 3 million more documents.

Already have an account? Log in

Document Summary

Sampling distributions for proportions confidence intervals for population proportions. When np and nq are at least 10, the normal distribution can be used to approximate the binomial distribution. We use the sample proportion, p^, as an estimate of the population proportion, p. A sample statistic is something we can calculate from a sample. We can take lots of samples and we will obtain different sample statistics that vary. A sampling distribution is the distribution of sample statistics. The sampling distribution shows us how much sample statistics vary from sample to sample. Confidence interval for estimating a population proportion, p. We use sample statistics to estimate population parameters. When we take a sample from a population and calculate a statistic (or point estimate) we are trying to estimate a population parameter: we use the point estimate p^ to estimate p. Often it is more informative to give an interval estimate for the parameter, rather than a point estimate.

Related Questions

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.

periwinkleyellowjacket100

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

STAT150 Lecture Notes - Lecture 5: Confidence Interval, Interval Estimation, Binomial Distribution

Document Summary

Get access

Related textbook solutions

Introductory Statistics

Related Documents

STAT150 Lecture Notes - Lecture 12: Investment Fund, Sports Betting

STAT150 Lecture Notes - Lecture 11: Null Hypothesis, Absenteeism

STAT150 Lecture Notes - Lecture 6: Point Estimation, Central Limit Theorem, Normal Distribution

Related Questions