The U.S. Office of Personnel Management reports that 51% of federal civilian employees have a bachelor's degree or higher (OPM.gov). A random sample of 95 employees in the private sector showed that 40 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 proportionsingle mean (a) What is the level of significance?State the null and alternate hypotheses. H0: p = 0.51; H1: p ≠ 0.51H0: μ = 0.51; H1: μ < 0.51 H0: μ = 0.51; H1: μ > 0.51H0: p = 0.51; H1: p > 0.51H0: p = 0.51; H1: p < 0.51H0: μ = 0.51; H1: μ ≠ 0.51 (b) What sampling distribution will you use? What assumptions are you making? The Student's t, since np > 5 and nq > 5.The standard normal, 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 > 0.2500.125 < P-value < 0.250 0.050 < P-value < 0.1250.020 < P-value < 0.0500.005 < P-value < 0.020P-value < 0.005

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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 U.S. Office of Personnel Management reports that 51% of federal civilian employees have a bachelor's degree or higher (OPM.gov). A random sample of 95 employees in the private sector showed that 40 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 proportionsingle mean

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: p = 0.51; H₁: p ≠ 0.51H₀: μ = 0.51; H₁: μ < 0.51 H₀: μ = 0.51; H₁: μ > 0.51H₀: p = 0.51; H₁: p > 0.51H₀: p = 0.51; H₁: p < 0.51H₀: μ = 0.51; H₁: μ ≠ 0.51

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

The Student's t, since np > 5 and nq > 5.The standard normal, 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 > 0.2500.125 < P-value < 0.250 0.050 < P-value < 0.1250.020 < P-value < 0.0500.005 < P-value < 0.020P-value < 0.005

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