Generally speaking, would you say that most people can be trusted? A random sample ofn₁=258people in Chicago ages18-25showed thatr₁=46said yes. Another random sample ofn₂=277people in Chicago ages35-45showed thatr₂=75said yes. Does this indicate that the population proportion of trusting people in Chicago is higher for the older group? Use= 0.05.

(a)What is the level of significance?

(b) State the null and alternate hypotheses.

• H₀:p₁=p₂;H₁:p₁<p₂
• H₀:p₁<p₂;H₁:p₁=p₂
• H₀:p₁=p₂;H₁:p₁p₂
• H₀:p₁=p₂;H₁:p₁>p₂

(c)What sampling distribution will you use? What assumptions are you making?

• The Student'st. The number of trials is sufficiently large.
• The standard normal. We assume the population distributions are approximately normal.
• The Student'st. We assume the population distributions are approximately normal.
• The standard normal. The number of trials is sufficiently large.
• What is the value of the sample test statistic? (Test the differencep₁p₂. Do not use rounded values. Round your final answer to two decimal places.)

(d)Find (or estimate) theP-value. (Round your answer to four decimal places.)

(e) Sketch the sampling distribution and show the area corresponding to theP-value.

(f)Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?

• At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
• At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
• At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
• At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

(g)Interpret your conclusion in the context of the application.

• Reject the null hypothesis, there is sufficient evidence that the proportion of trusting people in Chicago is higher in the older group.
• Fail to reject the null hypothesis, there is insufficient evidence that the proportion of trusting people in Chicago is higher in the older group.
• Reject the null hypothesis, there is insufficient evidence that the proportion of trusting people in Chicago is higher in the older group.
• Fail to reject the null hypothesis, there is sufficient evidence that the proportion of trusting people in Chicago is higher in the older group.