The researcher is primarily interested in their testing method identifying if μG has increased to μG = 4.25 micrograms. What is the Type 1 error rate of this testing strategy? Interpret this value in the context of the problem.
Added by Susan N.
Step 1
- The null hypothesis (H0) is that the mean concentration of μG is equal to 4.25 micrograms (μG = 4.25). - The alternative hypothesis (H1) is that the mean concentration of μG is greater than 4.25 micrograms (μG > 4.25). Show more…
Show all steps
Close
Your feedback will help us improve your experience
Keondre Parker and 78 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 94.6% of the people who have that disease. However, it erroneously gives a positive reaction in 4.1% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease" to answer the following questions. a. What is the probability of a Type I error? (Round your answer to 3 decimal places.) b. What is the probability of a Type II error? (Round your answer to 3 decimal places.)
Keondre P.
An investigator indicates that the POWER of his test (at a significance of 1%) of a sample mean resulting from his research is 0.87. What is the probability that he made a Type I error?
Christopher D.
An experimenter has prepared a drug dosage level that she claims will induce sleep for $80 \%$ of people suffering from insomnia. After examining the dosage, we feel that her claims regarding the effectiveness of the dosage are inflated. In an attempt to disprove her claim, we administer her prescribed dosage to 20 insomniacs and we observe $Y$, the number for whom the drug dose induces sleep. We wish to test the hypothesis $H_{0}: p=.8$ versus the alternative, $H_{a}: p<.8 .$ Assume that the rejection region $\{y \leq 12\}$ is used. a. In terms of this problem, what is a type I error? b. Find $\alpha$ c. In terms of this problem, what is a type II error? d. Find $\beta$ when $p=.6$ e. Find $\beta$ when $p=.4$
Hypothesis Testing
Elements of a Statistical Test
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD