1 / 13

# LESSON 13: SAMPLING DISTRIBUTION - PowerPoint PPT Presentation

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

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

## PowerPoint Slideshow about ' LESSON 13: SAMPLING DISTRIBUTION' - kelsie-kidd

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

Outline

• Central Limit Theorem

• Sampling Distribution of Mean

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.

Distribution of means of n random numbers, n=4

Distribution of means of n random numbers, n=10

• 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

• 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.

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?

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.

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.

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.

• For a small, finite population N, the formula for the standard deviation of sampling mean is corrected as follows:

Lesson 13