Are you here
Download
1 / 25

Are you here? - PowerPoint PPT Presentation


  • 78 Views
  • Uploaded on
  • Presentation posted in: General

Are you here?. Yes, and I’m ready to learn Yes, and I need a nap No. HW - Problem 6. When a truck load of apples arrives at a packing plant, a random sample of 125 is selected and examined for bruises, discoloration, and other defects.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha

Download Presentation

Are you here?

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Are you here?

  • Yes, and I’m ready to learn

  • Yes, and I need a nap

  • No


HW - Problem 6

  • When a truck load of apples arrives at a packing plant, a random sample of 125 is selected and examined for bruises, discoloration, and other defects.

  • The whole truckload will be rejected if more than 5% of the sample is unsatisfactory.

  • Suppose that in fact 9% of the apples on the truck do not meet the desired standard.

  • What is the probability that the shipment will be accepted anyway.


What is the probability that the shipment will be accepted anyway?

  • 0.062

  • 1-0.062

  • 0

  • 1

  • -1.54


Both of the sampling distributions we’ve looked at are Normal.

For proportions

For means

Standard Deviation


Standard Deviation vs. Standard Error

  • We don’t know p, μ, or σ, we’re stuck, right?

  • Nope. We will use sample statistics to estimate these population parameters.

  • Sample statistics are notated as: s,

  • Whenever we estimate the standard deviation of a sampling distribution, we call it a standard error.


For a sample proportion, the standard error is

For the sample mean, the standard error is

Standard Error


Exciting Statistics about ISU Students -2011 data

  • 69.1% of sexually active students use condoms

  • American College Health Association

  • n=272


A Confidence Interval


By the 68-95-99.7% Rule, we know

about 68% of all samples will have ’s within 1 SE of p

about 95% of all samples will have ’s within 2 SEs of p

about 99.7% of all samples will have ’s within 3 SEs of p

A Confidence Interval


Certainty vs. Precision


Certainty vs. Precision

  • The choice of confidence level is somewhat arbitrary, but keep in mind this tension between certainty and precision when selecting your confidence level.

  • The most commonly chosen confidence levels are 90%, 95%, and 99% (but any percentage can be used).


What Does “95% Confidence” Really Mean?

  • Each confidence interval uses a sample statistic to estimate a population parameter.

  • But, since samples vary, the statistics we use, and thus the confidence intervals we construct, vary as well.


What Does “95% Confidence” Really Mean? (cont.)

  • The figure to the right shows that some of our confidence intervals capture the true proportion (the green horizontal line), while others do not:


Homework Problem

  • A catalog sales company promises to deliver orders placed on the Internet within 3 days.

  • Follow-up calls to a few randomly selected customers show that a 95% CI for the proportion of all orders that arrive on time is 81% ± 4%


Which of the following statements is correct?

  • Between 77% and 85% of all orders arrive on time.

  • One can be 95% confident that the true population percentage of orders place on the Internet that arrive within 3 days is between 77% and 85%

  • One can be 95% confident that all random samples of customers will show that 81% of orders arrive on time

  • 95% of all random samples of customers will show that between 77% and 85% of orders arrive on time.


When the conditions are met, we are ready to find the confidence interval for the population proportion, p.

The confidence interval is

where

The critical value, z*, depends on the particular confidence level, C, that you specify.

One-Proportion z-Interval


Z* is the Critical Value

  • 80%  z*=1.282

  • 90% z*=1.645

  • 95% z*=1.96

  • 98%z*=2.326

  • 99% z*=2.576


Critical Values (cont.)

  • Example: For a 90% confidence interval, the critical value is 1.645:


HW – Problem 18

  • Often, on surveys there are two ways of asking the same question.

  • 1) Do you believe the death penalty is fair or unfairly applied?

  • 2) Do you believe the death penalty is unfair or fairly applied?


HW – Problem 18

  • Survey

  • 1) n=597

  • 2) n=597

  • For the second phrasing, 45% said the death penalty is fairly applied.


Suppose 54% of the respondents in survey #1 said the death penalty was fairly applied. Does this fall within a 95% confidence interval for survey #2?

  • Yes, it falls within my CI

  • No, it does not fall within my CI


Margin of Error: Certainty vs. Precision

  • The more confident we want to be, the larger our z* has to be

  • But to be more precise (i.e. have a smaller ME and interval), we need a larger sample size, n.

  • We can claim, with 95% confidence, that the interval contains the true population proportion.

    • The extent of the interval on either side of is called the margin of error (ME).

  • In general, confidence intervals have the form estimate± ME.


Margin of Error - Problem

  • Suppose the truth is that 56% of ISU student drink every weekend.

  • We want to create a 95% confidence interval, but we also want to be as precise as possible.

  • How many people should we sample?

  • How large should our margin of error be?


How many people should we sample to get a ME of 1%?

  • 1,000

  • Between 1,000 and 4,000

  • Between 4,000 and 8,000

  • Between 8,000 and 16,000


Upcoming work

  • Quiz #4 in class today

  • HW #8 due next Sunday

  • Part 3 of Data Project due April 2nd


ad
  • Login