7) The U.S. Bureau of Labor Statistics reports that 11.3% of U.S. workers belong

Question

7) The U.S. Bureau of Labor Statistics reports that 11.3% of U.S. workers belong to unions (BLS website, January 2014). Suppose a sample of 400 U.S. workers is collected in 2014 to determine whether union efforts to organize have increased union membership. a. Formulate the hypotheses that can be used to determine whether union membership increased in 2014. If the sample results show that 52 of the workers belonged to unions, what is the p-value for your hypothesis test? b. t = .05, what is your conclusion?

Explanation / Answer

a) here null hypothesis:Ho: p =0.113

alternate hypothesis: Ha: p>0.113

b) std error of proportion sep=(p(1-p)/n)1/2 =0.0158

sample proportion phat =52/400=0.13

threfore test statistic z =(phat-p)/sep =(0.13-0.113)/0.0158 =1.0739

for above test statistic ; p value =0.1414

c) as p value is greater than 0.05 level ; we can not reject null hypothesis.

we do not have sufficient evidence to cnclude that unifon efforts to organize have increased union membership.

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