question in image , please give legible or preferably typed response

1. A national survey showed that all people living in the United States exercise an average of 5.4 times per month. As a researcher studying health related behaviors, you want to know whether people living in New Jersey exercise more often, on average, than the total U.S. population. You take a sample of 210 New Jersey residents and find that the mean number of times per month that they exercise is 5.9 with a standard deviation of 3.0 times per month in this sample. Perform the appropriate, step-by-step, hypothesis test to determine whether, on average, people living in New Jersey exercise more often than the total U.S. population, at alpha = .01. Please include both the null and alternative hypothesis. State your conclusion in a complete sentence. 2. Thinking about the process of hypothesis testing, are you completely certain that you have come to the correct conclusion in problem? Explain why or why not. 3. As a sociologist, you want to assess whether levels of happiness differ between people who have many close friends and people who have few close friends. You administer a survey to 48 individuals who have many close friends and 57 people who have few close friends. In these samples, you find that those with many close friends have a mean score on a happiness scale of 78 (with a standard deviation of 9) while those who have few close friends have a mean score of 70 on the happiness scale (with a standard deviation of 12). Perform the appropriate hypothesis test to determine whether people who have many close friends differ from people who have few close friends in how happy they are with their lives, at alpha = .01. As before, please include both the null and alternative hypothesis and state your conclusions in a complete sentence