According to the Census Bureau, 18.1% of the people in the United States are of Hispanic or Latino origin. One county supervisor believes her county has a higher proportion of Hispanic people than the nation as a whole. She looked at their most recent survey data, which was a random sample of 437 county residents, and found that 44 of those surveyed were of Hispanic origin. Test your hypothesis at a 5% significance level ( =0.05).

1. State the hypotheses.
2. Check appropriate conditions for a hypothesis test.
3. Calculate P-value using z-table
4. State your conclusion.

2. In 1960, census results indicated that the age at which American men first married had a mean of 23.3 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage is different than in the 1960s. We plan to test our hypothesis by selecting a random sample of 40 men who married for the first time last year. The men in our sample married at an average age of 24.2 years, with a standard deviation of 5.3 years. Test your hypothesis at a 5% significance level ( =0.05).

1. Write appropriate hypotheses.
2. Do you think the necessary assumptions for inference are satisfied? (Check the conditions)
3. Compute the P-value using StatCrunch
4. What's your conclusion?

3. For each of the following situations, state whether a Type I, a Type II

1. A bank wants to know if the enrollment on their website is above 30% based on a small sample of customers. They test and reject the null hypothesis. Later they found out that actually 30% of all customers enrolled.
2. A human resource analyst wants to know if the applicants this year scored, on average, higher on their placement exam than the 52.5 points the candidates averaged last year. She sampled 50 recent tests and conducted a hypothesis test. She fails to reject the null hypothesis. At the end of the year, they found that the candidates this year had a mean of 55.3 points.