1. Introduction to Estimating Population Means
Copyright © 2008 by Hawkes Learning Systems/Quant Systems, Inc.
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HAWKES LEARNING SYSTEMS
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Section 8.1
Introduction to Estimating Population Means

2. HAWKES LEARNING SYSTEMS
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Confidence Intervals
8.1 Introduction to Estimating Population Means
Definitions:
Point Estimate – a single number estimate of a population parameter. The best point estimate of a population mean is the sample mean.
Interval Estimate – a range of possible values for the population parameter.
Level of Confidence, c – the degree of certainty that the interval estimate contains the population parameter. (e.g. 0.95, 0.99, etc.)
Confidence Interval – an interval estimate associated with a certain level of confidence.
Margin of Error, E – the largest possible distance from the point estimate that a confidence interval will cover.

3. The best point estimate of a population mean is the sample mean.
HAWKES LEARNING SYSTEMS
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Confidence Intervals
8.1 Introduction to Estimating Population Means
Find the best point estimate:
Find the best point estimate for the population mean of test scores on a standardized biology final exam. The following is a simple random sample taken from these test scores. 45 68 72 91
100 71 69 83 86 55 89 97 76 92 75 84 70 81 90 85 74 88 99 93 96
Solution:
The best point estimate of a population mean is the sample mean.

4. HAWKES LEARNING SYSTEMS
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Confidence Intervals
8.1 Introduction to Estimating Population Means
Confidence Interval for Population Means:

5. HAWKES LEARNING SYSTEMS
math courseware specialists
Confidence Intervals
8.1 Introduction to Estimating Population Means
Construct the confidence interval:
A college student researching study habits collects data from a random sample of 250 college students on campus and calculates that the sample mean is 15.7 hours per week. If the margin of error for the data using a 95% level of confidence is 2.2 hours, construct a 95% confidence interval for the data.
Solution:
Lower endpoint:
= 13.5 hours
Upper endpoint:
= 17.9 hours
13.5 <  < 17.9

6. HAWKES LEARNING SYSTEMS
math courseware specialists
Confidence Intervals
8.1 Introduction to Estimating Population Means
How to choose z or t:
σ is the population standard deviation
σ is known, n=30 or more,
and any distribution or
σ is known, n=29 or less,
and normally
distributed
choose z
σ is unknown,
normally distributed, and n=30 or more
σ is unknown,
normally distributed, and n=29 or less
choose z
choose t

7. σ is known, n=29 or less,
and normally
distributed

8. σ is known, n=30 or more

9. σ is known, n=29 or less,
and not normally
distributed

10. HAWKES LEARNING SYSTEMS
math courseware specialists
Confidence Intervals
8.1 Introduction to Estimating Population Means
How to choose z or t:
σ is the population standard deviation
σ is known, n=30 or more,
and any distribution or
σ is known, n=29 or less,
and normally
distributed
choose z
σ is unknown,
normally distributed, and n=30 or more
σ is unknown,
normally distributed, and n=29 or less
choose z
choose t

11. σ is unknown, not normally distributed

12. σ is unknown,
normally distributed, and n=29 or less

13. HAWKES LEARNING SYSTEMS
math courseware specialists
Confidence Intervals
8.1 Introduction to Estimating Population Means
How to choose z or t:
σ is the population standard deviation
σ is known, n=30 or more,
and any distribution or
σ is known, n=29 or less,
and normally
distributed
choose z
σ is unknown,
normally distributed, and n=30 or more
σ is unknown,
normally distributed, and n=29 or less
choose z
choose t

14. σ is unknown,
normally distributed, and n=29 or less

16. Lower = Mean – Margin of Error = 50 – 1.5 = 48.5
Upper = Mean + Margin of Error = = 51.5