1. EXAMPLE: The weight of a can of Coca Cola is supposed to have mean = 12 oz with std. dev.= 0.82 oz. The product is declared underweight if it weighs less than 10 oz.
With a random sample of one single Coke, find the probability that the can is underweight. (Assume a Normal Pop.)
With a SRS of 36 Cokes find the probability that the product averages will be underweight.
Collected by an SRS, and Approximately Normal -Stated.
Collected by an SRS, and Approximately Normal – n > 30 = CLT.

2. 25 c)
36 c) d)

5. Certainty vs. Precision

6. INTRODUCTION TO INFERENCE
CHAPTER 19
INTRODUCTION TO INFERENCE
Statistical Inference – A method of Drawing Conclusions from data.
The Two Types of Statistical Inference:
I. Confidence Interval – This is a method of estimating the true value of the population parameter by constructing an interval that captures the true parameter

7. Margin of Error - The true population parameter is within m% of the sample estimate, with some degree of confidence.

8. Confidence Interval for Proportions
Confidence Interval = Estimate ± Margin of Error

9. CONFIDENCE INTERVALS
Confidence Level – A level C confidence interval for a parameter is an interval computed from sample data by a method that in repeated sampling has probability C of producing an interval containing the true value of the parameter.
True Parameter
An 85% Confidence Level

10. (based on one sample) Interpreting 95% Confidence Interval
We are 95% Confident that the true parameter (proportion) {add context here} will be captured by the constructed interval ( ).
(based on one sample)

11. You ask 500 adults which of 2 candidates they support. =
You ask 500 adults which of 2 candidates they support. = .52 are in favor your candidate. Sketch a curve. Construct a 68% Confidence interval. Then Construct a 95% Confidence Interval.
.498
.542
.565
.475
.453
.587
.52
I am 99.7% Confident that the true population proportion of votes in favor of my candidate is between 45.3% and 58.7%.
I am 68% Confident that the true population proportion of votes in favor of my candidate is between 49.8% and 54.2%.
I am 95% Confident that the true population proportion of votes in favor of my candidate is between 47.5% and 56.5%.

12. HW: PAGE 446: 1-5
He believes the true proportion of voters with a certain opinion is within 4% of his estimate.
He believes the true percentage of children who are exposed to lead-base paint is within 3% of his estimate.

13. HW: PAGE 446: 1-5

17. company vehicles are fuel efficient?
EXAMPLE: A large national company wants to keep costs down so it purchases fuel efficient vehicles. An SRS of 40 vehicles are selected and it is found that 28 of them are classified “Fuel Efficient”, what percent of the entire
company vehicles are fuel efficient?
1. Estimate the population parameter with a 90% Confidence Interval and Interpret it.
2. Estimate the population parameter with a 99% Confidence Interval and Interpret it.
We can be 90% confident that the true population proportion of fuel efficient vehicles in the company is between 58.1% and 81.9%.
We can be 99% confident that the true population proportion of fuel efficient vehicles in the company is between 51.3% and 88.7%.

18. Confidence Intervals for a Population Proportion: The Level C Confidence Interval for p-hat is computed by:
To Interpret a Confidence Interval we say, “We can be 95% confident that the true population proportion is
between a and b.”

19. What Does “85% Confidence” Really Mean?
The figure to the right shows that some of our confidence intervals capture the true proportion (the green horizontal line), while others do not:

20. Critical Value ( z* ) – The number of standard deviation away from the mean with probability p lying to the right under the standard normal curve is called the Upper p critical value. C% P P
-z* z*
Confidence Intervals for a Population Proportion: The Level C Confidence Interval for p-hat is computed by:
where z* is the upper (1 – C)/2 critical value found by: z* = | INVNORM( (1 – C)/2 ) | or by Table.

21. Sampling Distribution of Pennies2 4 9 14 21 27 66
142 13
1958
1963
1968
1973
1978
1983
1988
1993
1998
2003
2008
150 –
125 –
100 –
75 –
50 –
25 –
0 –
Penny’s Date