1 / 11

Chapter 21

Chapter 21. STA 200 Summer I 2011. Previously. A parameter is a number that describes the population. In practice, we won’t know its value. Additionally, the parameter is constant (its value does not change ).

frye
Télécharger la présentation

Chapter 21

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 21 STA 200 Summer I 2011

  2. Previously • A parameter is a number that describes the population. In practice, we won’t know its value. Additionally, the parameter is constant (its value does not change). • A statistic is a number that describes a sample. A statistic can vary from sample to sample. We will know the value of a statistic. • Sampling variability is the idea that the value of a statistic will vary from one sample to another.

  3. Sampling Distribution of • The sampling distribution of is the distribution of values taken by in all possible samples of the same size. • If the sample size is large enough: • the sampling distribution of is approximately normal • the mean is p • the standard deviation is

  4. 68-95-99.7 Rule • Since the sampling distribution of is approximately normal, the 68-95-99.7 Rule applies. • If we sample repeatedly, about 95% of the values of will be within two standard deviations of p, by the 68-95-99.7 Rule.

  5. 68-95-99.7 Rule • Symbolically, p will be captured by the interval from to 95% of the time. • We can be a little more accurate: for 95% confidence, it’s really 1.96 standard deviations not 2. • Thus, the formula becomes .

  6. One Final Adjustment • In practice, we won’t know the value of p, so we’ll have to guess at it. If we have to guess a specific value, the best guess is . • The formula for a 95% confidence interval is:

  7. Example • In a random sample of 687 college students, 419 indicated that they favored having the option of receiving pass-fail grades for elective courses. • Construct a 95% confidence interval for p, the proportion of all college students who favor the option of pass-fail grades for elective courses.

  8. Other Confidence Levels • The confidence level doesn’t have to be 95%; you can have any confidence level between 0% and 100%. • The other commonly used confidence levels are 90% and 99%.

  9. Generalized Confidence Interval Formula • The generalized formula for confidence intervals is: • z* is called the critical value, which is dependent on the confidence level. • Common Critical Values:

  10. More Examples • Construct a 99% confidence interval for the pass-fail example. • Note: A higher confidence level requires a larger margin of error (and, therefore, a wider interval). A lower confidence level requires a smaller margin of error (and, therefore, a narrower interval).

  11. More Examples (cont.) • An airline wants to determine the proportion of passengers that bring only carry-on luggage. In a random sample of 300 passengers, 31% have only carry-on luggage. • Find a 90% confidence interval for the proportion of all passenger who have only carry-on luggage. • Note: A larger sample size results in a smaller margin of error (and vice versa).

More Related