Question

You may need to use the appropriate appendix table or technology to answer this question.

An agency reports that 11.6% of workers in a particular country belonged to unions. Suppose a sample of 400 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 ≤ 0.116

H_a: p > 0.116

H₀: p > 0.116

H_a: p ≤ 0.116

    

H₀: p = 0.116

H_a: p ≠ 0.116

H₀: p ≥ 0.116

H_a: p < 0.116

H₀: p < 0.116

H_a: p ≥ 0.116

(b)

If the sample results show that 52 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

α = 0.05,

what is your conclusion?

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

Answer 1

The statistical software output for this problem is :

H₀: p ≤ 0.116

H_a: p > 0.116

Test statistics = 0.87

P-value = 0.1910

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

in union membership.