A study found that, in 2005, 12.5% of U.S. workers belonged to unions. Suppose a

Question

A study found that, in 2005, 12.5% of U.S. workers belonged to unions. Suppose a sample of 400 U.S. workers is collected in 2017 to determine whether union efforts to organize have increased union membership. (a) Formulate the hypothesis that can be used to determine whether union membership increased in 2017 (b) If the sample results show that 52 workers in the sample belonged to unions, will you reject or fail to reject the null hypothesis using the critical value approach at the alpha = 0.05 level. Explain your reasoning. (c) Would you reject or fail to reject the null hypothesis using the p-value approach at the alpha = 0.05 level? Explain your reasoning

Explanation / Answer

here null hypothesis: p=12.5%=0.125

and alternate hypothesis: p>0.125

b) here std error =(p(!-p)/n)1/2 =0.0165

also phat =52/400 =0.13

hence test stat z=(phat-p)/std error =(0.13-0.125)/0.0165 =0.3024

critical value at 0.05 level =1.645

as test stat is not in critical region we can not reject null hypothesis

c) for above test stat p value =0.3812

as p value is greater then 0.05 level we can not reject null hypothesis

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