1 / 13

LESSON 13: SAMPLING DISTRIBUTION

LESSON 13: SAMPLING DISTRIBUTION. Outline Central Limit Theorem Sampling Distribution of Mean. CENTRAL LIMIT THEOREM.

kelsie-kidd
Download Presentation

LESSON 13: SAMPLING DISTRIBUTION

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. LESSON 13: SAMPLING DISTRIBUTION Outline • Central Limit Theorem • Sampling Distribution of Mean

  2. CENTRAL LIMIT THEOREM Central Limit Theorem: If a random sample is drawn from any population, the sampling distribution of the sample mean is approximately normal for a sufficiently large sample size. The larger the sample size, the more closely the sampling distribution of will resemble a normal distribution.

  3. Distribution of random numbers

  4. Distribution of means of n random numbers, n=4

  5. Distribution of means of n random numbers, n=10

  6. SAMPLING DISTRIBUTION OF THE SAMPLE MEAN • If the sample size increases, the variation of the sample mean decreases. • Where, = Population mean = Population standard deviation = Sample size = Mean of the sample means = Standard deviation of the sample means

  7. SAMPLING DISTRIBUTION OF THE SAMPLE MEAN • Summary: For any general distribution with mean and standard deviation • The distribution of mean of a sample of size can be approximated by a normal distribution with • Exercise: Generate 1000 random numbers uniformly distributed between 0 and 1. Consider 200 samples of size 5 each. Compute the sample means. Check if the histogram of sample means is normally distributed and mean and standard deviation follow the above rules.

  8. SAMPLING DISTRIBUTION OF THE SAMPLE MEAN Example 1: An automatic machine in a manufacturing process requires an important sub-component. The lengths of the sub-component are normally distributed with a mean, =120 cm and standard deviation, =5 cm. What does the central limit theorem say about the sampling distribution of the mean if samples of size 4 are drawn from this population?

  9. SAMPLING DISTRIBUTION OF THE SAMPLE MEAN Example 2: An automatic machine in a manufacturing process requires an important sub-component. The lengths of the sub-component are normally distributed with a mean, =120 cm and standard deviation, =5 cm. Find the probability that one randomly selected unit has a length greater than 123 cm.

  10. SAMPLING DISTRIBUTION OF THE SAMPLE MEAN Example 3: An automatic machine in a manufacturing process requires an important sub-component. The lengths of the sub-component are normally distributed with a mean, =120 cm and standard deviation, =5 cm. Find the probability that, if four units are randomly selected, their mean length exceeds 123 cm.

  11. SAMPLING DISTRIBUTION OF THE SAMPLE MEAN Example 4: An automatic machine in a manufacturing process requires an important sub-component. The lengths of the sub-component are normally distributed with a mean, =120 cm and standard deviation, =5 cm. Find the probability that, if four units are randomly selected, all four have lengths that exceed 123 cm.

  12. CORRECTION FOR SMALL SAMPLE SIZE • For a small, finite population N, the formula for the standard deviation of sampling mean is corrected as follows:

  13. READING AND EXERCISES Lesson 13 Reading: Sections 8-1, 8-2, 8-3, pp. 260-276 Exercises: 9-3,9-4, 9-8, 9-17, 9-19

More Related