According to some sources, roughly 25% of Americans volunteer their time to nonprofits. A community organizer wants to know if his local community is inconsistent with that gure. He takes a sufficiently large random sample and obtains a test statistic of -2. (a) Find the p-value for his test: (3 decimal places) (b) What should he conclude at a = .01? Ho. The people in his community seem to volunteer less than the rest of the nation. There is not enough evidence to conclude that the proportion of people who volunteer in his community is inconsistent with the national figure. He can conclude that there is a difference in the proportion of people in his community that volunteer and the proportion of the country that volunteers. There is evidence to indicate that 25% of the people in his community volunteer. MY NOTES Suppose a statistics professor is performing a hypothesis test of Ho: p = .69 vs. Ha: p > .69. He finds a test statistic of z = 1.60 and a p-value of .055. (a) What does his test statistic mean? The typical distance from the mean is 1.6. 1.6% of his sample had the trait for which he was testing. The probability of getting a sample like this was 1.6%. His test statistic was 1.50 standard errors away from his sample proportion, His sample proportion was 1.60 standard errors greater than .69. (b) Interpret his p-value. If the true proportion was .69, he would get a sample proportion at least as large as what he observed with a probability of .055. His sample proportion must have been within .055 of the population proportion. The true value of the parameter is .055. If the true proportion is really .69, the probability that the null hypothesis is true is .055. You want to know if your crush is in love with you. Being a diligent scientist (at least for the time being), you elect to approach the situation as a hypothesis test, where the null hypothesis is that your crush m (a) In this context, describe a Type 11 error. You conclude that your crush loves you, and your crush does love you. You conclude that your crush does not love you, and your crush really does not love you. You conclude your crush does not love you, but your crush actually does love you. You conclude that your crush loves you, but your crush does not love you. (b) You want to minimize the probability of concluding your crush likes you and confessing your admiration when your crush does not, in fact, love you back. What standard of evidence would be best? a = .10 because it is the largest. a = .05 because it is most balanced. a = .01 because it is the smallest. DETAILS Do people that do not go to college travel less? Suppose that the average number of countries visited for those with a college degree is right-skewed with mean = 5.1. We take a random sample of 63 individuals who did not attend college and nd a sample mean of 416 with a standard deviation of 0191 (a) Identify the correct hypotheses to test the question posed at the beginning of the problem. Hal )4 - 9 Ha: 14 a (b) Why should we trust the hypothesis test procedure we are about to use? The sample size is at least 30. There are at least 15 successes and 15 failures The distribution of the sample can be inferred to be bell-shaped. The population should be approximately normal. (c) What is the test statistic for this test? (3 decimal places) (d) Using the test statistic we found in part c), we would find the p-value for this test using --- 8 --- 8