Question

[Understanding of hypothesis testing]

The College of Engineering would like to know if the mean incoming freshman ACT (America College Test) score for 2018 is statistically different than the mean ACT score across the country.

*State the null (H0) and alternative (H1) statistical hypotheses to address this question.

*If the College wants to be 95% confident in any conclusion, what is the value of the significance criterion?

*If the College expects a 90% likelihood of detecting a difference among means, when one actually exists, what is the allowable Type II error rate?

*A “false alarm” in hypothesis testing represents what states of reality and analyst judgment?

Answer 1

*State the null (H0) and alternative (H1) statistical hypotheses to address this question.

H0: The mean incoming freshman ACT (America College Test) score for 2018 is equal to the mean ACT score across the country.

H0: The mean incoming freshman ACT (America College Test) score for 2018 is different than the mean ACT score across the country.

*If the College wants to be 95% confident in any conclusion, what is the value of the significance criterion?

The Significance criterion = (100 - 95) % = 5%

*If the College expects a 90% likelihood of detecting a difference among means, when one actually exists, what is the allowable Type II error rate?

Type II error rate = Probability of accepting the null hypothesis given that it is false = 1 - Probability of rejecting the null hypothesis given that it is false = 1 - 0.9 = 0.1

So, Type II error rate = 10%

*A “false alarm” in hypothesis testing represents what states of reality and analyst judgment?

A false alarm is where you receive a positive result for a test, when you should have received a negative results. It’s also called “false positive”. In statistics, a false positive is usually called a Type I error. A type I error is when you incorrectly reject the null hypothesis. This creates a “false positive” for your research, leading you to believe that your hypothesis (i.e. the alternate hypothesis) is true, when in fact it isn’t.