A 2011 survey, by the Bureau of Labor Statistics, reported that 91% of Americans have

paid leave. In January 2012, a random survey of 1000 workers showed that 89% had

paid leave.

The resulting p-value is .0271; thus, the null hypothesis is rejected. It is concluded that

there has been a decrease in the proportion of people, who have paid leave from 2011 to

January 2012.

What type of error is possible in this situation?

A. type I

B. type II

C. neither

D. both

A. Type I error.

Step-by-step explanation:

Hello!

The hypotheses tested were "the proportion of people who have paid leave has decreased" vs "the proportion of people who have paid leave has either increased or hasn't changed"

The researcher obtained a p-value of 0.0271 and rejected the null hypothesis. The study concluded that the proportion of people on paid leave has decreased.

When conducting a hypothesis test there are four possible situations derived from the combination of the decisions made and the nature of the hypothesis:

1. Reject the null hypothesis when the hypothesis is false (This is a correct decision) (True positive, TP)

2. Reject the null hypothesis when the hypothesis is true (This decision is also known as Type I error) (False positive, FP)

3. Fail to reject the null hypothesis when the hypothesis is true (This is a correct decision) (True negative, TN)

4. Fail to reject the null hypothesis when the hypothesis is false (This decision is also known as Type II error) (False negative, FN)

Each of these decisions has an associated probability:

1. P(TP)= 1-β (Known as the power of the test)

2. P(FP)= α (Known as significance level)

3. P(TN)= 1-α

4. P(FN)= β

In this example, since the decision made was to reject the null hypothesis, so the researcher may stand in two possible positions, one is that he took the right decision and the second one is that he rejected a true null hypothesis. The type of error he might commit is a Type I error with an associated probability of α.

I hope it helps!

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step-by-step explanation:

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