An agency reports that 11.5% of workers in a particular country belonged to unions. Suppose a sample of 300 workers is collected to determine whether union efforts to organize have increased union membership. (a) Formulate the hypotheses that can be used to determine whether union membership has increased. H0: p ≥ 0.115 Ha: p < 0.115 H0: p = 0.115 Ha: p ≠ 0.115 H0: p ≤ 0.115 Ha: p > 0.115 H0: p < 0.115 Ha: p ≥ 0.115 H0: p > 0.115 Ha: p ≤ 0.115 (b) If the sample results show that 42 of the workers belonged to unions, what is the p-value for your hypothesis test? Find the value of the test statistic. (Round your answer to two decimal places.) ( ) Find the p-value. (Round your answer to four decimal places.) p-value = ( ) (c) At ? = 0.05, what is your conclusion? Do not reject H0. There is insufficient evidence to conclude that there has been an increase in union membership. Reject H0. There is sufficient evidence to conclude that there has been an increase in union membership. Reject H0. There is insufficient evidence to conclude that there has been an increase in union membership. Do not reject H0. There is sufficient evidence to conclude that there has been an increase in union membership.

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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An agency reports that 11.5% of workers in a particular country belonged to unions. Suppose a sample of 300 workers is collected to determine whether union efforts to organize have increased union membership.

(a)

Formulate the hypotheses that can be used to determine whether union membership has increased.

H₀: p ≥ 0.115

H_a: p < 0.115

H₀: p = 0.115

H_a: p ≠ 0.115

H₀: p ≤ 0.115

H_a: p > 0.115

H₀: p < 0.115

H_a: p ≥ 0.115

H₀: p > 0.115

H_a: p ≤ 0.115

(b)

If the sample results show that 42 of the workers belonged to unions, what is the p-value for your hypothesis test?

Find the value of the test statistic. (Round your answer to two decimal places.)

( )

Find the p-value. (Round your answer to four decimal places.)

p-value = ( )

(c)

At ? = 0.05,
what is your conclusion?

Do not reject H₀. There is insufficient evidence to conclude that there has been an increase in union membership.

Reject H₀. There is sufficient evidence to conclude that there has been an increase in union membership.

Reject H₀. There is insufficient evidence to conclude that there has been an increase in union membership.

Do not reject H₀. There is sufficient evidence to conclude that there has been an increase in union membership.

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