Question

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 = 41 said yes. Another random sample of n2 = 280 people in Chicago ages 35-45 showed that r2 = 75 said yes. Does this indicate that the population proportion of trusting people in Chicago is higher for the older group? Use α = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. H0: p1 = p2; H1: p1 ≠ p2 H0: p1 = p2; H1: p1 < p2 H0: p1 = p2; H1: p1 > p2 H0: p1 < p2; H1: p1 = p2 (b) What sampling distribution will you use? What assumptions are you making? The Student's t. The number of trials is sufficiently large. The standard normal. We assume the population distributions are approximately normal. The Student's t. 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 difference p1 − p2. Do not use rounded values. Round your final answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (d) 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 α? At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. 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. Reject the null hypothesis, there is sufficient evidence that the proportion of trusting people in Chicago is higher in the older group

Answer 1

Does this indicate that the population proportion of trusting people in Chicago is higher for the older group? Use α = 0.05.

Given that,

n1 = people in Chicago ages 18-25 = 250

r1 = 41

n2 = number of people in Chicago ages 35-45 = 280

r2 = 75

(a) What is the level of significance? State the null and alternate hypotheses.

Here we have to test the hypothesis that,

H0 : p1 = p2 Vs H1 : p1 > p2

where p1 and p2 are two population proportions.

Assume alpha = level of significance = 0.05

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

The standard normal. The number of trials is sufficiently large.

Assumptions :

• The sampling method for each population is simple random sampling.
• The samples are independent.
• Each sample includes at least 10 successes and 10 failures.
• Each population is at least 20 times as big as its sample.

What is the value of the sample test statistic? (Test the difference p1 − p2. Do not use rounded values. Round your final answer to two decimal places.)

This is two sample proportion z-test.

We can do this test in ti-83 calculator.

steps :

STAT --> TESTS --> 6:2-PropZTest --> ENTER --> Input all the values --> Select alternative : > --> ENTER --> Calculate -->ENTER

Test statistic = -2.89

(c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot

P-value = 0.9981

Draw critical region steps in ti-83 :

STAT --> TESTS --> 6:2-PropZTest --> ENTER --> Input all the values --> Select alternative : > --> ENTER -->Draw --> ENTER

This will gives us shaded area.

P-value > alpha

Accept H0 at 5% level of significance.

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

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