UNIT 6

– CONFID

ENCE

INTE

RVALS

SECTI

ONS 6.1

AND 6

.2

CONFIDENCE INTERVALS

When we take a sample and calculate the mean of a sample it will be used to estimate the population parameter.

CONFIDENCE INTERVALS

In order to determine the number of points a new high blood pressure medicine reduces a patient’s systolic measurement . A sample of 6 patients were given the medicine and their blood pressure was measured after the prescribe period of time. The number of points the blood pressure was reduce is listed below.

12 5 13 0 -1 19

Calculate the Mean

CONFIDENCE INTERVALSThe pharmaceutical company knows the results of the high blood pressure medicine will •React differently on another group of patients. •When they report the results, they want to use an interval.•They said we are 95% confidence the new blood pressure medicine will reduce patient’s blood pressure between 2 and 14 points.

MARGIN OF ERROR

The distance from the sample mean and the lower and upper limits.

Mean = 8Lower limit = 2 8 – 2 = 6Upper limit = 14 14 – 8 = 6Margin of Error = MOE = 6

HOW TO CALCULATE THE MARGIN OF ERROR

We know how to calculate the mean. Today we will discuss how to calculate the Margin of error.

LARGE SAMPLE CONFIDENCE INTERVALS FOR MEANS

LARGE SAMPLE CONFIDENCE INTERVALS FOR MEANS

LARGE SAMPLE CONFIDENCE INTERVALS FOR MEANS

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PAGE 319 51

A publisher wants to estimate the mean length of time (in minutes) all adults spend reading newspapers. To determine this estimate, the publisher takes a random sample of 15 people and obtains the following results.11, 9, 8, 10, 10, 9, 7, 11, 11, 7, 6, 9, 10, 8, 10

From past studies, the publisher assumes σ is 1.5 minutes and that the population of times is normally distributed.

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11, 9, 8, 10, 10, 9, 7, 11, 11, 7, 6, 9, 10, 8, 10

Calculate the meanWe will calculate a 99%

Confidence IntervalSubtract 99% from 1

Divide by 2

Find the Z value from the Table 4.

What is the population standard deviation σ?

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11, 9, 8, 10, 10, 9, 7, 11, 11, 7, 6, 9, 10, 8, 10

Sample Mean = 9.07 Z = 2.575σ = 1.5What is the sample size n?

Calculate the square root of n?

MOE = Z *σ/√n =

PAGE 319 51

11, 9, 8, 10, 10, 9, 7, 11, 11, 7, 6, 9, 10, 8, 10

Sample Mean = 9.07 Z = 2.575σ = 1.5 MOE = .997 ≈ 1.00

Lower Limit = Sample Mean – MOEUpper Limit = Sample Mean + MOE

We are 99% confident that the mean length of time an adult reads the paper is between …

CONFIDENCE INTERVAL

What happens if • Sample size n < 30• Population standard deviation

is unknown.The Margin of Error formula

must be changed to MOE = t*s/√n

T DISTRIBUTION

The t distribution was developed for small samples number (n < 30). It has characteristic similar to the normal distribution.•Symmetric, Mean = Median = Mode•Bell Shaped•Extends forever to the left and the right.

PAGE #11

CONFIDENCE INTERVAL – SMALL SAMPLE SIZE

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CONFIDENCE INTERVAL