sst5e_ppt_ch08.pptx

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STATISTICS

INFORMED DECISIONS USING DATA

Fifth Edition, Global Edition

Chapter 8

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8.1 Distribution of the Sample Mean

Learning Objectives

1. Describe the distribution of the sample mean: normal

population

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8.1 Distribution of the Sample Mean

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8.1 Distribution of the Sample Mean

Introduction

(2 of 2)

The

sampling distribution

of a statistic is a probability

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8.1 Distribution of the Sample Mean

Illustrating Sampling Distributions

(1 of 3)

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8.1 Distribution of the Sample Mean

Illustrating Sampling Distributions

(2 of 3)

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8.1 Distribution of the Sample Mean

Illustrating Sampling Distributions

(3 of 3)

Step 3:

Assuming that we are sampling from a finite

population, repeat Steps 1 and 2 until all distinct

simple random samples of size

n

have been

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8.1 Distribution of the Sample Mean

8.1.1 Describe the Distribution of the Sample Mean: Normal

Population

(1 of 14)

Parallel Example 1: Sampling Distribution of the Sample

Mean-Normal Population

The weights of pennies minted after 1982 are approximately

normally distributed with mean 2.46 grams and standard deviation

0.02 grams.

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8.1 Distribution of the Sample Mean

8.1.1 Describe the Distribution of the Sample Mean: Normal

Population

(2 of 14)

The data on the following slide represent the sample means

for the 200 simple random samples of size

n

= 5.

For example, the first sample of

n

= 5 had the following data:

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8.1 Distribution of the Sample Mean

8.1.1 Describe the Distribution of the Sample Mean: Normal

Population

(3 of 14)

Sample Means for Samples of Size

n

= 5

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8.1 Distribution of the Sample Mean

8.1.1 Describe the Distribution of the Sample Mean: Normal

Population

(4 of 14)

Sample Means for Samples of Size

n

= 5

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8.1 Distribution of the Sample Mean

8.1.1 Describe the Distribution of the Sample Mean: Normal

Population

(5 of 14)

The mean of the 200 sample means is 2.46, the same as the

mean of the population.

The standard deviation of the sample means is 0.0086,

which is smaller than the standard deviation of the

population.

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8.1 Distribution of the Sample Mean

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8.1 Distribution of the Sample Mean

8.1.1 Describe the Distribution of the Sample Mean: Normal

Population

(7 of 14)

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8.1 Distribution of the Sample Mean

8.1.1 Describe the Distribution of the Sample Mean: Normal

Population

(8 of 14)

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8.1 Distribution of the Sample Mean

8.1.1 Describe the Distribution of the Sample Mean: Normal

Population

(9 of 14)

Parallel Example 2: The Impact of Sample Size on

Sampling Variability

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8.1 Distribution of the Sample Mean

8.1.1 Describe the Distribution of the Sample Mean: Normal

Population

(10 of 14)

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8.1 Distribution of the Sample Mean

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8.1 Distribution of the Sample Mean

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8.1 Distribution of the Sample Mean

8.1.1 Describe the Distribution of the Sample Mean: Normal

Population

(13 of 14)

Parallel Example 3: Describing the Distribution of the

Sample Mean

The weights of pennies minted after 1982 are approximately

normally distributed with mean 2.46 grams and standard deviation

0.02 grams.

What is the probability that in a simple random sample of 10

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8.1 Distribution of the Sample Mean

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8.1 Distribution of the Sample Mean

8.1.2 Describe the Distribution of the Sample Mean:

Nonnormal Population

(1 of 9)

The following table and histogram

give the probability distribution for

rolling a fair die:

Face on Die

Relative Frequency

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8.1 Distribution of the Sample Mean

8.1.2 Describe the Distribution of the Sample Mean:

Nonnormal Population

(2 of 9)

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8.1 Distribution of the Sample Mean

8.1.2 Describe the Distribution of the Sample Mean:

Nonnormal Population

(6 of 9)

• The shape of the distribution of the sample mean becomes

approximately normal as the sample size

n

increases,

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8.1 Distribution of the Sample Mean

8.1.2 Describe the Distribution of the Sample Mean:

Nonnormal Population

(7 of 9)

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8.1 Distribution of the Sample Mean

8.1.2 Describe the Distribution of the Sample Mean:

Nonnormal Population

(8 of 9)

Parallel Example 5: Using the Central Limit Theorem

Suppose that the mean time for an oil change at a “10-minute oil

change joint” is 11.4 minutes with a standard deviation of 3.2

minutes.

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8.1 Distribution of the Sample Mean

8.1.2 Describe the Distribution of the Sample Mean:

Nonnormal Population

(9 of 9)

Parallel Example 5: Using the Central Limit Theorem

b)

If a random sample of

n

= 35 oil changes is selected, what is

the probability the mean oil change time is less than 11