Generally speaking, would you say that most people can be trusted? A random sample of n1 = 250 people in Chicago ages 18–25 showed that r1 = 45 said yes. Another random sample of n2 = 280 people in Chicago ages 35–45 showed that r2 = 71 said yes (based on information from the National Opinion Research Center, University of Chicago). Does this indicate that the population proportion of trusting people in Chicago is higher for the older group? Use α = 0.05.
Please provide the following information:
(a) What is the level of significance? State the null and alternate hypotheses.
(b) What sampling distribution will you use? What assumptions are you making? Compute the sample test statistic.
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a)–(c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(e) Interpret your conclusion in the context of the application.