Answered: The U.S. Bureau of Labor Statistics…

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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Question

The U.S. Bureau of Labor Statistics reports that 11.6% of U.S. workers belonged to unions in 2020. A random sample of U.S. workers collected in 2021 to determine whether union efforts to organize have increased union membership found 14% belonged to a union.

(a) Which hypotheses should be used to test if the proportion of U.S. workers who belonged to unions has increased since 2020?
H₀:
H_a:

(b) The standard error is 0.0189. How should this be interpreted?
The standard error is the average distance between a     and the     .

(c) What is the test statistic? (4 decimals)

(d) What is the p-value? (4 decimals)

(e) How should this p-value be interpreted?

This is the probability that the true proportion of U.S. workers belonged to unions has stayed the same.This is the probability that the true proportion of U.S. workers belonged to unions has increased. This is the probability of getting a sample proportion of 0.14 or greater, assuming the true proportion of U.S. workers belonged to unions has stayed the same.This is the probability of getting a sample proportion of 0.116 or greater, assuming the true proportion of U.S. workers belonged to unions has increased.

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