1 / 1

NOTE: Variable must be approximately normally distributed

ANATOMY OF A CONFIDENCE INTERVAL FOR m WHERE n < 30. When SIGMA, s , is KNOWN and n < 30. When SIGMA, s , is UNKNOWN and n < 30. NOTE: Variable must be normally distributed

Download Presentation

NOTE: Variable must be approximately normally distributed

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. ANATOMY OF A CONFIDENCE INTERVAL FOR m WHERE n < 30 When SIGMA, s, is KNOWN and n < 30 When SIGMA, s, is UNKNOWN and n < 30 NOTE: Variable must be normally distributed EXAMPLE: A random sample of 19 women results In a mean height of 63.85 inches. Other studies have shown that women’s heights are normally distributed with a standard deviation of 2.5 inches. Construct a 90% confidence interval for the mean height of all women. NOTE: Variable must be approximately normally distributed EXAMPLE: In a time study, 20 randomly selected managers were found to spend a mean time of 2.40 hrs. per day on paperwork. The standard deviation of the scores is 1.30 hours. Construct a 98% confidence interval for the mean time spent on paperwork by all managers. In this example we are given a standard deviation and normality based on prior studies. Given that sigma is known, the variable is normally distributed and n < 30 we can use the formula: In this example we are given a standard deviation based on a sample of n = 20. Therefore we will use the formula: From the given information we have From the given information we have s = 2.5 There the value of is obtained from the t- distribution table for the given confidence level which corresponds to: and confidence level = 90% or .90 which corresponds to: The 98% confidence interval for m is given by: The 90% confidence interval for m is given by: (here: 2.4 - .738 = 1.662 hrs. and 2.4 + .738 = 3.138 hrs.) (here: 63.85 - .943 = 62.907 in. and 63.85 + .943 = 64.793 in.) In Words: We are 90% confident that the mean height of women lies between 62.907 inches and 64.793 inches. In Words: We are 98% confident that the mean hours spend on paperwork by managers is between 1.662 hours and 3.138 hours. In Notation: The 90% confidence interval for m may be presented in any of three ways: In Notation: The 98% confidence interval for m may be presented in any of three ways: or or or [inches] or [hours]

More Related