Posted by **Katie** on Monday, November 11, 2013 at 2:52pm.

The U.S. Department of Labor and Statistics released the current unemployment rate of 5.3% for the month in the U.S. and claims the unemployment has not changed in the last two months. However, the states statistics reveal that there is a decrease in the U.S. unemployment rate. A test on unemployment was done on a random sample size of 1000 and found 38 people were unemployed. Should the state continue with its assumption of no change? Test an appropriate hypothesis using α = 0.05.

A) P-value = 0.0171. The state should continue with its assumption. There is a 1.7% chance of having 38 or less of 1000 people in a random sample be unemployed if in fact 5.3% do.

B) P-value = 0.983. The change is statistically significant. A 98% confidence interval is (2.4%, 5.2%). This is clearly lower than 5.3%. The chance of observing 38 or less unemployed people of 1000 is 98% if the unemployment is really 5.3%.

C) P-value = 0.98. The state should continue with its assumption. There is a 98% chance of having 38 or less of 1000 people in a random sample be unemployed if in fact 5.3% do.

D) P-value = 0.0171. The change is statistically significant. A 90% confidence interval is (2.8%, 4.8%). This is clearly lower than 5.3%. The chance of observing 38 or less unemployed people of 1000 is 1.7% if the unemployment is really 5.3%. The P-value is less than the alpha level of 0.05.

E) P-value = 0.0342. The change is statistically significant. A 90% confidence interval is (2.8%, 4.8%). This is clearly lower than 5.3%. The chance of observing 38 or less unemployed people of 1000 is 3.4% if the unemployment is really 5.3%.

Huh?