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**preview**shows pages 1-2. to view the full**7 pages of the document.**MATH 1P98-Chapter 9

Two Proportions

Objectives:

1. Test a claim about two population proportions or

2. Construct a confidence interval estimate of the difference between two population

proportions

Notation:

For Population 1 we let

P1= population proportion

N1= size of sample

X1= Number of Successes in the sample

(Sample proportion)

(complement of P(hat)1 )

Pooled Sample Proportion

The pooled sample proportion is given by and is given by

Requirements:

1. The sample proportions are from two simple random samples that are independent.

2. For each of the two samples there are atleast 5 successes and 5 failures

Test Statistic for Two Proportions

where p1 -p2 = 0 (null hypothesis)

Sample proportions

( pooled sample proportion) and

P-Value or Critical Value

Confidence Interval Estimate of p1-p2

The confidence interval estimate of the difference p1-p2 is

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

Margin of error is given by:

Hypothesis Tests

-We only consider tests having a null hypothesis of P1=P2 ( so the null hypothesis is given as

H0:p1=p2.

-Can be done using a P-Value or Critical Value

-Find the p value of the test statistic, if it’s less than the test statistic then reject the null

hypothesis

Confidence Intervals

Use the format given earlier. If the confidence interval estimate does not include 0, we have

evidence suggesting that P1 and P2 have different values.

Cautions:

1. When testing a claim about two proportions, the critical value and p value method

are equivalent, but they are not equivalent to the confidence interval method. If you

want to test a claim about two population proportions use the p-value or critical

value method. If you want to estimate the difference between two population

proportions use a confidence interval.

2. Don’t test for equality of two population proportions by determining whether there

is an overlap between two individual confidence interval estimates of the two

individual population proportions. When compared to the confidence interval

estimate of p1-p2, the analysis of overlap between the two individual confidence

intervals is more conservative (by rejecting equality less often) and it has less

power(it is less likely to reject p1-p2 when in reality p1≠p2)

Two Means: Independent Samples

Part 1: Independent Samples with σ1 and σ2 unknown and Not assumed equal

This section involves two independent samples, and the following section deals with

samples that are deprendent. It is important to know the difference between independent

samples and dependent samples.

Independent: If the sample values from one population are not related to or somehow

naturally paired or matched with the sample values from the other population

Dependent: If the sample values are somehow matched, where the matching is based on

some inherent relationship. ( Each pair of sample values consists of two measurements from

the same subject such as before/after data or each pair of sample values consists of matched

pairs- such as husband/wife data where the matching is based on some meaningful

relationship.

Hypothesis Test/ Confidence Interval for two independent Means

Notation:

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