The Congressional Budget Office reports that 36% of federal civilian employees have a bachelor's degree or higher (The Wall Street Journal). A random sample of 117 employees in the private sector showed that 31 have a bachelor's degree or higher. Does this indicate that the percentage of employees holding bachelor's degrees or higher in the private sector is less than in the federal civilian sector? Use α = 0.05. What are we testing in this problem? single proportion single mean (a) What is the level of significance? State the null and alternate hypotheses. H0: μ = 0.36; H1: μ > 0.36 H0: μ = 0.36; H1: μ ≠ 0.36 H0: p = 0.36; H1: p ≠ 0.36 H0: p = 0.36; H1: p < 0.36 H0: p = 0.36; H1: p > 0.36 H0: μ = 0.36; H1: μ < 0.36 (b) What sampling distribution will you use? What assumptions are you making? The standard normal, since np > 5 and nq > 5. The Student's t, since np > 5 and nq > 5. The standard normal, since np < 5 and nq < 5. The Student's t, since np < 5 and nq < 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find (or estimate) the P-value. P-value > 0.250 0.125 < P-value < 0.250 0.050 < P-value < 0.125 0.025 < P-value < 0.050 0.005 < P-value < 0.025 P-value < 0.005 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 = 0.05 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 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 not statistically significant. (e) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.05 level to conclude that the proportion of bachelor or higher degrees in the private sector is less than in the federal civilian sector.There is insufficient evidence at the 0.05 level to conclude that the proportion of bachelor or higher degrees in the private sector is less than in the federal civilian sector.

The Congressional Budget Office reports that 36% of federal civilian employees have a bachelor's degree or higher (The Wall Street Journal). A random sample of 117 employees in the private sector showed that 31 have a bachelor's degree or higher. Does this indicate that the percentage of employees holding bachelor's degrees or higher in the private sector is less than in the federal civilian sector? Use α = 0.05. What are we testing in this problem? single proportion single mean (a) What is the level of significance? State the null and alternate hypotheses. H0: μ = 0.36; H1: μ > 0.36 H0: μ = 0.36; H1: μ ≠ 0.36 H0: p = 0.36; H1: p ≠ 0.36 H0: p = 0.36; H1: p < 0.36 H0: p = 0.36; H1: p > 0.36 H0: μ = 0.36; H1: μ < 0.36 (b) What sampling distribution will you use? What assumptions are you making? The standard normal, since np > 5 and nq > 5. The Student's t, since np > 5 and nq > 5. The standard normal, since np < 5 and nq < 5. The Student's t, since np < 5 and nq < 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find (or estimate) the P-value. P-value > 0.250 0.125 < P-value < 0.250 0.050 < P-value < 0.125 0.025 < P-value < 0.050 0.005 < P-value < 0.025 P-value < 0.005 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 = 0.05 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 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 not statistically significant. (e) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.05 level to conclude that the proportion of bachelor or higher degrees in the private sector is less than in the federal civilian sector.There is insufficient evidence at the 0.05 level to conclude that the proportion of bachelor or higher degrees in the private sector is less than in the federal civilian sector.

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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The Congressional Budget Office reports that 36% of federal civilian employees have a bachelor's degree or higher (The Wall Street Journal). A random sample of 117 employees in the private sector showed that 31 have a bachelor's degree or higher. Does this indicate that the percentage of employees holding bachelor's degrees or higher in the private sector is less than in the federal civilian sector? Use α = 0.05.

What are we testing in this problem?

single proportion

single mean

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: μ = 0.36; H₁: μ > 0.36

H₀: μ = 0.36; H₁: μ ≠ 0.36

H₀: p = 0.36; H₁: p ≠ 0.36

H₀: p = 0.36; H₁: p < 0.36

H₀: p = 0.36; H₁: p > 0.36

H₀: μ = 0.36; H₁: μ < 0.36

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

The standard normal, since np > 5 and nq > 5.

The Student's t, since np > 5 and nq > 5.

The standard normal, since np < 5 and nq < 5.

The Student's t, since np < 5 and nq < 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c) Find (or estimate) the P-value.

P-value > 0.250

0.125 < P-value < 0.250

0.050 < P-value < 0.125

0.025 < P-value < 0.050

0.005 < P-value < 0.025

P-value < 0.005

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 = 0.05 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 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 not statistically significant.

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

There is sufficient evidence at the 0.05 level to conclude that the proportion of bachelor or higher degrees in the private sector is less than in the federal civilian sector.
There is insufficient evidence at the 0.05 level to conclude that the proportion of bachelor or higher degrees in the private sector is less than in the federal civilian sector.

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