Question

A local newspaper article reported that at least 50% of the construction jobs in the metropolitan New Orleans area are being filled by undocumented foreign workers. Anna Reed believes the actual percentage is much lower than that, and intends to challenge the newspaper’s figure. She took a random sample of 100 construction workers and found that 42 of them are undocumented.

1) What is the margin of error of the survey at the 95% level of confidence?

2) Find a 95% confidence interval for the true proportion π of undocumented construction workers in the metropolitan New Orleans area.

3) Test her alternate hypothesis that the proportion of undocumented construction workers in this area is significantly less than 50%.

(i) Alternatives

Select one: H0: π ≤ 0.5 H1: π > 0.5 H0: π ≥ 0.5 H1: π < 0.5 H0: π ≠ 0.5 H1: π = 0.5 H0: π = 0.5 H1: π ≠ 0.5 None of the other four

ii) Test statistic

Select one:

None of the other four z* = 1.645 z* = 1.80 z* = 1.96 z* = 2.10 (iii) p-value Select one: 0.0227 0.04 0.0548 0.9452 None of the other four

(iv) What is the conclusion if the level of significance is α=0.05?

Select one:

Conclude H0 that the proportion of undocumented construction workers in this area is not significantly less than 50%.

Conclude H0 that the proportion of undocumented construction workers in this area is significantly less than 50%.

Conclude H1 that the proportion of undocumented construction workers in this area is not significantly less than 50%.

Conclude H1 that the proportion of undocumented construction workers in this area is significantly less than 50%. None of the other four

Answer 1

Conclude H0 that the proportion of undocumented construction workers in this area is not significantly less than 50%.