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3. Are the following statements TRUE or FALSE. If they are FALSE, explain why and correct the statement. 2 (a) If we choose a higher confidence level, then we get a narrower confidence inter- val. (b) If we need weaker evidence for rejecting Hỏ, then we should pick a smaller sig- nificance level. (c) In creasing the sample size in general results in a higher power to reject a false Ho. (d) The significance level a is the probability of rejecting a false Ho. (e) Type I and type II errors are related. A decrease in the probability of one type of error always results in an increase in the probability of the other, provided that the sample size n does not change (f) The power of a statistical test is the probability of failing to reject the null hy- pothesis Ho when the alternative hypothesis is true

3. Are the following statements TRUE or FALSE. If they are FALSE, explain why and correct the statement. 2 (a) If we choose a higher confidence level, then we get a narrower confidence inter- val. (b) If we need weaker evidence for rejecting Hỏ, then we should pick a smaller sig- nificance level. (c) In creasing the sample size in general results in a higher power to reject a false Ho. (d) The significance level a is the probability of rejecting a false Ho. (e) Type I and type II errors are related. A decrease in the probability of one type of error always results in an increase in the probability of the other, provided that the sample size n does not change (f) The power of a statistical test is the probability of failing to reject the null hy- pothesis Ho when the alternative hypothesis is true

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Question 3:** **Are the following statements TRUE or FALSE? If they are FALSE, explain why and correct the statement.** --- (a) If we choose a higher confidence level, then we get a narrower confidence interval. (b) If we need weaker evidence for rejecting \( H_0 \), then we should pick a smaller significance level. (c) Increasing the sample size in general results in a higher power to reject a false \( H_0 \). (d) The significance level \( \alpha \) is the probability of rejecting a false \( H_0 \). (e) Type I and Type II errors are related. A decrease in the probability of one type of error always results in an increase in the probability of the other, provided that the sample size \( n \) does not change. (f) The power of a statistical test is the probability of failing to reject the null hypothesis \( H_0 \) when the alternative hypothesis is true.
Transcribed Image Text:**Question 3:** **Are the following statements TRUE or FALSE? If they are FALSE, explain why and correct the statement.** --- (a) If we choose a higher confidence level, then we get a narrower confidence interval. (b) If we need weaker evidence for rejecting \( H_0 \), then we should pick a smaller significance level. (c) Increasing the sample size in general results in a higher power to reject a false \( H_0 \). (d) The significance level \( \alpha \) is the probability of rejecting a false \( H_0 \). (e) Type I and Type II errors are related. A decrease in the probability of one type of error always results in an increase in the probability of the other, provided that the sample size \( n \) does not change. (f) The power of a statistical test is the probability of failing to reject the null hypothesis \( H_0 \) when the alternative hypothesis is true.
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