Unit 8 Section 7.4

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

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,

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.

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?

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?

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.

Section 7.4 Homework: Pg 390-391: 3 – 15 ODD