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Consider a one-sample t-test with significance level a for the null hypothesis Ho: μ = 0 vs. the alternative H₁: 0. Consider the following statements: (i) If the critical value is increased, the probability of type II errors increases. (ii) The critical value is chosen so that the probability of type II errors is small. (iii) The critical value is chosen so that the probability of type I errors is small. (iv) If the critical value is increased, the probability of type I errors increases. (v) Type I errors are always more likely than type II errors. Which of these statements are true?

Consider a one-sample t-test with significance level a for the null hypothesis Ho: μ = 0 vs. the alternative H₁: 0. Consider the following statements: (i) If the critical value is increased, the probability of type II errors increases. (ii) The critical value is chosen so that the probability of type II errors is small. (iii) The critical value is chosen so that the probability of type I errors is small. (iv) If the critical value is increased, the probability of type I errors increases. (v) Type I errors are always more likely than type II errors. Which of these statements are true?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 8CR
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Explain why （iii）is true， （ii）is false ，riguousl y

A7 Consider a one-sample t-test with significance level a for the null hypothesis Ho: μ = 0 vs. the alternative H₁: μ0. Consider the following statements: (i) If the critical value is increased, the probability of type II errors increases. (ii) The critical value is chosen so that the probability of type II errors is small. (iii) The critical value is chosen so that the probability of type I errors is small. (iv) If the critical value is increased, the probability of type I errors increases. (v) Type I errors are always more likely than type II errors. Which of these statements are true?
Transcribed Image Text:A7 Consider a one-sample t-test with significance level a for the null hypothesis Ho: μ = 0 vs. the alternative H₁: μ0. Consider the following statements: (i) If the critical value is increased, the probability of type II errors increases. (ii) The critical value is chosen so that the probability of type II errors is small. (iii) The critical value is chosen so that the probability of type I errors is small. (iv) If the critical value is increased, the probability of type I errors increases. (v) Type I errors are always more likely than type II errors. Which of these statements are true?
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