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?

The correct answer is 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%.

To determine whether the state should continue with its assumption of no change in the unemployment rate, a hypothesis test needs to be conducted using a significance level (α) of 0.05. The hypothesis to be tested is as follows:

Null hypothesis (H0): The unemployment rate is equal to 5.3%.
Alternative hypothesis (H1): The unemployment rate is not equal to 5.3%.

Based on the test conducted on a random sample of 1000 people, where 38 were unemployed, we can calculate the p-value. This is the probability of observing a sample result as extreme or more extreme than the one obtained, assuming the null hypothesis is true.

The correct answer is:

A) P-value = 0.0171. The state should continue with its assumption. There is a 1.7% chance of having 38 or fewer unemployed individuals out of a sample of 1000 if the actual unemployment rate is 5.3%.

To answer this question, we need to perform a hypothesis test to determine if the observed unemployment rate is significantly different from the assumed unemployment rate of 5.3%.

The null hypothesis (H0) assumes that there is no change in the unemployment rate, while the alternative hypothesis (H1) assumes that there is a change in the unemployment rate.

Since we are given a p-value, we can compare it to the significance level (α) to determine if we should reject or fail to reject the null hypothesis.

Let's look at the options provided:

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%.

First, let's focus on the p-value. The p-value is a measure of the probability of obtaining the observed data, or more extreme, given that the null hypothesis is true. In this case, the observed data is 38 unemployed individuals out of a sample size of 1000.

The significance level (α) is given as 0.05, which means that we are willing to accept a 5% chance of rejecting the null hypothesis when it is true.

Comparing the p-values in the options:

Option A has a p-value of 0.0171.
Option B has a p-value of 0.983.
Option C has a p-value of 0.98.
Option D has a p-value of 0.0171.
Option E has a p-value of 0.0342.

Considering the significance level of 0.05, it is observed that options A and D have p-values less than 0.05. This means that both options suggest rejecting the null hypothesis, indicating a significant change in the unemployment rate.

Among these options, option D also mentions a lower chance of observing 38 or fewer unemployed individuals in a sample of 1000 if the unemployment rate is really 5.3%. This aligns with the hypothesis test.

Therefore, option D is the correct answer:

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.

The state should not continue with its assumption of no change in the unemployment rate.