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EPA and Statistics self-efficacy

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1. The Environmental Protection Agency (EPA) is testing tap water in one community. If they find evidence that the average level of lead is greater than 15 parts per billion (ppb) they will order that the water be turned off and that residents be given free bottled water until the problem is fixed.
A. State the null and alternative hypotheses that the agency is testing. Use proper notation.

B. What does a Type I error mean in this situation? What are the consequences of making a Type I error here?

C. What does a Type II error mean in this situation? What are the consequences of making a Type II error here?

D. In this scenario, is a Type I or Type II error more serious? Explain your reasoning.

E. If you were working for the EPA and running this research study, what alpha level would you use and why?

2. An online statistics instructor wants to know if students' statistics self-efficacy increases from the beginning to end of an online introductory statistics course. Through the American Statistical Association (ASA) she finds 49 other researchers who are also interested in this topic. Together they organize a series of 50 research studies comparing online introductory students' statistics self-efficacy at the beginning and end of a semester.

A. If there is not difference between students' statistics self-efficacy at the beginning and end of the semester, how many tests would you expect to be statistically significant at the 0.05 alpha level just by random chance?

B. If you were conducting one of these research studies, what alpha level would you use and why?

C. Suppose that of 50 tests, there were 24 tests with statistically significant results. Would this be convincing evidence that statistics self-efficacy changes from beginning to end of a semester? Explain why or why not.

D. If only the 24 tests with statistically significance results were published, and not the 26 tests without statistically significant results, explain why publication bias is a problem.

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Solution Summary

The Solution finds the null and alternative hypotheses, as well as identifies what Type I and II errors would be for the example. Answered in 522 words.

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1A.
H0 : x ̅ ≤ 15
Ha : x ̅ > 15

B.
A Type I error is the mistake of rejecting the null hypothesis when the null hypothesis is actually true. In this situation, it means that the EPA believes that the average level of lead is greater than 15 ppb, and orders that water to be turned off and that residents be given free bottles of water until the problem is fixed, when, in reality, the average level of lead is not greater than 15 ppb.

The consequences of making a Type I error are that money and time are spent unnecessarily, and resources are wasted.

C.
A Type II error is the mistake of failing to reject the null hypothesis when the null hypothesis is actually false. In this situation, it means that the EPA believes that the average ...

Solution provided by:
J Pye, MSc
Education
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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