(d) You run the analysis and the p-value is 0.9, α = 0.001 and β = 0.01. If you fail to reject H0, What is the probability that you made the wrong decision in this case? (e) Under what conditions could an expert witness give the following statement based solely on lead bullet statistical evidence: “The bullet fragments must have come from the same box or from another box that would have been made by the same company on the same day.”
Please answer parts (d) and (e) using a two independent samples hypothesis t test
(Q4). You are a crime scene investigator trying to match the lead content of bullet fragments found at a crime scene to the lead content of a box of bullets found with a suspect. To simplify this question, assume that the instrument you use gives you one measurement per fragment in grams/cm3. Assume that you have 5 measurements from fragments found at the crime scene and 7 measurements from bullets found with the suspect.
(a) What type of hypothesis test will you use?
(b) What are H0 and Ha? Write them both mathematically and in words.
(c) You run the analysis and the p-value is 0.0001 and α = 0.001, and β = 0.9. If you reject H0, what is the
(d) You run the analysis and the p-value is 0.9, α = 0.001 and β = 0.01. If you fail to reject H0, What is the probability that you made the wrong decision in this case?
(e) Under what conditions could an expert witness give the following statement based solely on lead bullet statistical evidence: “The bullet fragments must have come from the same box or from another box that would have been made by the same company on the same day.”
Part d)
Given information :
P-value = 0.001.
α , it is the probability of a type I error, or rejecting the null hypothesis when it is true and it is given as 0.001.
β , is the opposite; the probability of of accepting the null hypothesis when it's false and it is given as 0.01.
Here you're asked to find the probability that you made the wrong decision in this case.
Based on above information , we can say that it is type II error.
Thus , the probability of a Type II error is the β = 0.01.
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