Skill #12

I can understand potential Type I and Type II errors and explain them in the context of a situation.

The percentage of all high school graduates that enroll in college is 66%. In a random sample of 200 high school graduates from a certain county, 53% enrolled in college. To test if there is enough evidence that the percentage of high school graduates who enroll in college is lower in this county, the hypotheses are Ho: p = 0.66 and 7л: p < 0.66.

Concluding that the percentage of high school graduates in this county enrolling in college is not lower than 66%, but in fact it is lower.

According to the Centers for Disease Control and Prevention, 16% of all children aged 6 to 11 years are overweight. A school nurse thinks that the percentage of 6- to 11-year-olds who are overweight in their local school district is higher.

Your hypotheses, therefore, are Ho: p = 0.16 and Ha: p > 0.16.

Concluding that the percentage of overweight children in their district is more than 16%, but in fact it is not more than 16%.

Null hypothesis (Ho): Defendant is innocent

Alternative Hypothesis (Ha): Defendant is guilty

What could be the type 1 error be?

Declaring defendant not guilty when they are

Null hypothesis (Ho): Defendant is innocent

Alternative Hypothesis (Ha): Defendant is guilty

What could be the type 2 error be?

Declaring defendant guilty when they are not.

Type I Error:

Rejecting the Ho, given the Ha is actually true.

Type II Error:

Not rejecting Ho, given Ha is actually true