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Inferences about two proportions. Inferences about two proportions. Notation: For Sample 1 population proportion size of sample number of successes Note: , , and used for sample 2. Inferences about two proportions. Pooled sample proportion is denoted by:.

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Inferences about two proportions1
Inferences about two proportions

Notation:

For Sample 1

  • population proportion

  • size of sample

  • number of successes

    Note: , , and used for sample 2.


Inferences about two proportions2
Inferences about two proportions

Pooled sample proportion is denoted by:


Inferences about two proportions3
Inferences about two proportions

Requirements

  • Samples are from two independent random samples

  • The number of successes and failures are at least 5 each.

    Test statistic:


Inferences about two proportions4
Inferences about two proportions

Hypothesis Tests:

  • State Claims and Hypotheses.

    ( and is that they are different)

    2. Find test statistics

    3. Draw picture and find p-value.

    4. Make a decision. (Compare p-value and

    5. Summarize results


Inferences about two proportions5
Inferences about two proportions

The table below lists results from a simple random sample of front seat occupants involved in car crashed. Use a 0.05 significance level to test the claim that the fatality rate of occupants is lower for those in cares equipped with airbags.


Inferences about two proportions6
Inferences about two proportions

In Cleveland, a sample of 73 mail carries show that 10 had been bitten by an animal during one week. In Philadelphia, in a sample of 80 mail carries, 16 had received animal bites. Is there a significant difference in the proportions? Use a to test the claim that the proportions are not equal.


Inferences about two proportions7
Inferences about two proportions

In a sample of 80 Americans, 55% wished they were rich. In a sample of 90 Europeans, 45% wished that they were rich. At 0.05 significance level test the claim that the proportion of Europeans that wish to be rich is less than that of Americans


Inferences about two proportions8
Inferences about two proportions

A sample of 200 teenagers shows that 50 believe that war is inevitable, and sample of 300 people over age 60 shows that 93 believe war is inevitable. Test the claim that the proportion of teenagers who believe war is inevitable is greater than that of people over age 60.


Inferences about two proportions9
Inferences about two proportions

HOMEWORK!!!

9-2: 13-23 odd.


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