Download presentation

Presentation is loading. Please wait.

Published byMarlee Freedman Modified over 2 years ago

2
Parameter: A number describing a characteristic of the population (usually unknown) The mean gas price of regular gasoline for all gas stations in Maryland

3
The mean gas price in Maryland is $______ Statistic: A number describing a characteristic of a sample.

4
In Inferential Statistics we use the value of a sample statistic to estimate a parameter value.

5
We want to estimate the mean height of MC students. The mean height of MC students is 64 inches

6
Will x-bar be equal to mu? What if we get another sample, will x-bar be the same? How much does x-bar vary from sample to sample? By how much will x-bar differ from mu? How do we investigate the behavior of x-bar?

7
What does the x-bar distribution look like?

8
Graph the x-bar distribution, describe the shape and find the mean and standard deviation

9
Rolling a fair die and recording the outcome Simulation randInt(1,6) Press MATH Go to PRB Select 5: randInt(1,6)

10
Rolling a die n times and finding the mean of the outcomes. Mean(randInt(1,6,10) Press 2 nd STAT[list] Right to MATH Select 3:mean( Press MATH Right to PRB 5:randInt( Let n = 2 and think on the range of the x-bar distribution What if n is 10? Think on the range

11
Rolling a die n times and finding the mean of the outcomes. The Central Limit Theorem in action

15
For the larger sample sizes, most of the x-bar values are quite close to the mean of the parent population mu. (Theoretical distribution in this case) This is the effect of averaging When n is small, a single unusual x value can result in an x-bar value far from the center With a larger sample size, any unusual x values, when averaged with the other sample values, still tend to yield an x-bar value close to mu. AGAIN, an x-bar based on a large will tends to be closer to mu than will an x-bar based on a small sample. This is why the shape of the x-bar distribution becomes more bell shaped as the sample size gets larger.

16
Normal Distributions

17
The Central Limit Theorem in action Closing stock prices ($) Variability of sample means for samples of size 64 26 – 2.5 26 + 2.5 26 + 2*2.5 __|________|________|________X________|________|________|__ 18.5 21 23.5 26 28.5 31 33.5

18
Closing stock prices ($) Variability of sample means for samples of size 64 2.5% | 95% | 2.5% 26 – 2.5 26 + 2.5 26 + 2*2.5 __|________|________|________X________|________|________|__ 18.5 21 23.5 26 28.5 31 33.5 About 99.7% of samples of 64 closing stock prices have means that are within $7.50 of the population mean mu About 95% of samples of 64 closing stock prices have means that are within $5 of the population mean mu

19
We want to estimate the mean closing price of stocks by using a SRS of 64 stocks. Assume the standard deviation σ = $20. X ~Right Skewed (μ = ?, σ = 20) __|________|________|________X________|________|________|__ μ-7.5 μ-5 μ-2.5 μ μ+2.5 μ+5 μ+7.5 We’ll be 95% confident that our estimate is within $5 from the population mean mu We’ll be 99.7% confident that our estimate is within $7.50 from the population mean mu

23
Simulation Roll a die 5 times and record the number of ONES obtained: randInt(1,6,5) Press MATH Go to PRB Select 5: randInt(1,6,5)

24
Roll a die 5 times, record the number of ONES obtained. Do the process n times and find the mean number of ONES obtained. The Central Limit Theorem in action

25
Use website APPLETS to simulate proportion problems

Similar presentations

Presentation is loading. Please wait....

OK

AP Statistics 9.3 Sample Means.

AP Statistics 9.3 Sample Means.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google