Use the Traditional (Critical Value) Method In a random sample of 500 people aged 20-24, 22% were smokers. In a random sample of 450 people aged 25-29, 14 were smokers. Test the claim that the proportion of smokers in the two age groups is the same. Use a significance leve of 0.01. List the knowns, p1- hat, p2 - hat, n1 and n2. • the null and alternative hypothesis, • the critical value, • the pooled estimate, • the test statistics and • draw the graph and label the test statistic, critical value and rejection regions. Reject or fail to reject? State the conclusion as outlined in the book or hvnothesis test template

A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage, u, of foodservice workers in the U.S. Last year's mean hourly wage was $8.08, and there is reason to believe that this year's value is different from last year's. The union decides to do a statistical test to see if the value has indeed changed. The union chooses a random sample of this year's wages, computes the mean of the sample to be $8.48, and computes the standard deviation of the sample to be $1.25. Based on this information, answer the questions below. What are the null hypothesis (H) and the alternative hypothesis (H,) that should be used for the test? H: u is [? |H: u is ? ? In the context of this test, what is a Type II error? A Type II error is ? v the hypothesis that u is ? when, in fact, u is ? Suppose that the union decides to reject the null hypothesis. What sort of error might it be making? ?

A research firm reported that 15% of those surveyed described their health as poor26as good, 40as very goodand 19% excellent. A professional in Chicago wanted to determine people in Chicago had similar feelings toward their health. a sample of people in Chicago, 70 described their health as poor as good, 220 as very good and excellent Using = 0.05.complete a hypothesis test to determine the distribution is different from the firm's report. Show all steps to hypothesis testing,

Last year, 41% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 32% planned to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 55 business owners.  Suppose the business owners in the sample do as they plan. Conduct a hypothesis test that can be used to determine whether the proportion of business owners providing holiday gifts had decreased from last year. State the hypotheses.