1 / 8

7.2 Confidence Intervals

7.2 Confidence Intervals . When SD is unknown. The value of  , when it is not known, must be estimated by using s , the standard deviation of the sample.

harris
Télécharger la présentation

7.2 Confidence Intervals

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. 7.2 Confidence Intervals When SD is unknown

  2. The value of , when it is not known, must be estimated by using s, the standard deviation of the sample. When s is used, especially when the sample size is small (less than 30), critical values greater than the values for are used in confidence intervals in order to keep the interval at a given level, such as the 95%. These values are taken from the t Distribution

  3. 1. It is bell-shaped. 2. It is symmetric about the mean. 3. The mean, median, and mode are equal to 0 and are located at the center of the distribution. 4. The curve never touches the x axis. 5. The variance is greater than 1. (SD > 1) 6. The t distribution is actually a family of curves based on the concept of degrees of freedom, which is related to sample size. 7. As the sample size increases, the t distribution approaches the standard normal distribution. Characteristics of the t Distribution

  4. The degrees of freedom for a confidence interval for the mean are found by subtracting 1 from the sample size. That is, d.f. = n – 1. • Example: If the sample size is 30, the d.f. will be 29. Degrees of Freedom (d.f.)

  5. Formula for a Specific Confidence Interval for the Mean When  is unknown and n < 30 The degrees of freedom are n – 1. We will use the table in the back page of the book to help us with this formula.

  6. Find the tα/2 value for a 95% confidence interval when the sample size is 22. Degrees of freedom are d.f.= 21.

  7. Ten randomly selected people were asked how long they slept at night. The mean time was 7.1 hours, and the standard deviation was 0.78 hours. Find the 95% confidence interval of the mean time. Assume the variable is normally distributed.

  8. Practice: p. 374 5, 12, 13, 14, 15, 16, 18

More Related