Generally speaking, would you say that most people can be trusted? A random sample of n1 = 254 people in Chicago ages 18-25 showed that r1 = 47 said yes. Another random sample of n2 = 282 people in Chicago ages 35-45 showed that r2 = 67 said yes. Does this indicate that the population proportion of trusting people in Chicago is higher for the older group? Use α = 0.10. (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. 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. 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. (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 = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. 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 insufficient 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. Fail to reject the null hypothesis, there is sufficient evidence that the proportion of trusting people in Chicago is higher in the older group.

Generally speaking, would you say that most people can be trusted? A random sample of n1 = 254 people in Chicago ages 18-25 showed that r1 = 47 said yes. Another random sample of n2 = 282 people in Chicago ages 35-45 showed that r2 = 67 said yes. Does this indicate that the population proportion of trusting people in Chicago is higher for the older group? Use α = 0.10. (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. 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. 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. (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 = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. 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 insufficient 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. Fail to reject the null hypothesis, there is sufficient evidence that the proportion of trusting people in Chicago is higher in the older group.

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Description: Generally speaking, would you say that most people can be trusted? A random sample of n1 = 254 people in Chicago ages 18-25 showed that r1 = 47 said yes. Another random sample of n2 = 282 people in Chicago ages 35-45 showed that r2 = 67 said yes. Doe

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Generally speaking, would you say that most people can be trusted? A random sample of n₁ = 254 people in Chicago ages 18-25 showed that r₁ = 47 said yes. Another random sample of n₂ = 282 people in Chicago ages 35-45 showed that r₂ = 67 said yes. Does this indicate that the population proportion of trusting people in Chicago is higher for the older group? Use α = 0.10.

(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. 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.

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.

(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 = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

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

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 insufficient 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.

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

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