Question

a) The U.S. Bureau of Labor Statistics reports that 11.5% of U.S. workers belong to unions. Suppose a sample of 300 U.S. workers is collected in 2014 to determine whether union efforts to organize have increased union membership. The sample results show that 49 of the workers belonged to unions. Compute the test statistics.

b) The U.S. Bureau of Labor Statistics reports that 10% of U.S. workers belong to unions. Suppose a sample of 400 U.S. workers is collected in 2014 to determine whether union efforts to organize have increased union membership. The sample results show that 41 of the workers belonged to unions. Compute the p-value.

c) The U.S. Bureau of Labor Statistics reports that 11.3% of U.S. workers belong to unions. Suppose a sample of 400 U.S. workers is collected in 2014 to determine whether union efforts to organize have increased union membership at 0.025 level of significance. The sample results in a test statistic (z) of 1.46. We conclude that union membership increased in 2014. (Enter 1 if the conclusion is correct. Enter 0 otherwise.)

Answer 1

a)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.1633 - 0.115)/sqrt(0.115*(1-0.115)/300)
z = 2.62

b)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.1025 - 0.1)/sqrt(0.1*(1-0.1)/400)
z = 0.17

P-value Approach
P-value = 0.4325

c)

This is aright tailed test

z = 1.46

This is right tailed test, for α = 0.025
Critical value of z is 1.96.
Hence reject H0 if z > 1.96

Answer is 0