Question

An agency reports that historically 11.7% of workers in a particular country belong 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 ≤ 0.117

H_a: p > 0.117

H₀: p < 0.117

H_a: p ≥ 0.117

    

H₀: p > 0.117

H_a: p ≤ 0.117

H₀: p = 0.117

H_a: p ≠ 0.117

H₀: p ≥ 0.117

H_a: p < 0.117

(b)

If the sample results show that 36 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?

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 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.

Answer 1

a)

Ho :   p ≤ 0.117
H1 :   p >   0.117

b)

Number of Items of Interest,   x =   36                  
Sample Size,   n =    300                  
                          
Sample Proportion ,    p̂ = x/n =    0.1200                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.019                  
Z Test Statistic = ( p̂-p)/SE = (   0.1200   -   0.117   ) /   0.0186   =   0.16
                          

p-Value   =   0.4358 [Excel function =NORMSDIST(-z)              

c)

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