1. Unit 8
Section 7.4

2. 7.4: Hypothesis Testing for Proportions
A hypothesis test involving a population proportion can be considered a binomial experiment.
There are two outcomes
Recall…
μ = np
σ= √npq

3. Test value = (Observed Value)-(expected value)
Section 7.4
Proportions also involve finding a z-score
Recall:
Test value = (Observed Value)-(expected value)
Standard error
Thus,

4. Section 7.4 Steps for Using a z-test for a Proportion
Verify that the sampling distribution can be approximated by a normal distribution.
State the hypotheses and identify the claim.
Identify the level of significance (σ).
Find the critical values(s).
Determine the rejection region(s).
Find the standardized test statistic (z-score)
Make a decision.
Interpret the decision.

5. Section 7.4
Example 1: An educator estimates that the dropout rate for seniors at high schools in New Jersey is 15%. Last year, 38 seniors from a random sample of 200 New Jersey seniors withdrew. At α = 0.05, is there enough evidence to reject the educator’s claim?

6. Section 7.4
Example 2: A telephone company representative estimates that 40% of its customers have call waiting service. To test this hypothesis, she selected a sample of 100 customers and found that 37% have call waiting. At α = 0.01, is there enough evidence to reject the claim?

7. Section 7.4
Example 3: A statistician read that at least 77% of the population oppose replacing $1 bills with $1 coins. To see if the claim is valid, the statistician selected a sample of 80 people and found that 55 were opposed to replacing the $1 bills. At α = 0.01, test the claim that at least 77% of the population are opposed to the change.

8. Section 7.4
Homework:
Pg : 3 – 15 ODD