Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error?

Question

A manufacturer claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation of 3.3mg. Identify the type II error for the test.

Answer 1

Ho: σ = 3.3 mg

Ha: σ ≠ 3.3 mg

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Type I Error: We reject a true null.



The manufacture determines that the true standard

deviation of the amount of acetaminophen is not 3.3 mg,

even thought it is 3.3 mg.

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Type II Error: We fail to reject a false null.



The manufacture determines that the true standard

deviation of the amount of acetaminophen is 3.3 mg,

even thought it isn't.

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I will not be offended by you.

Answer 2

enable’s start up from scratch. I even have right here a bag of marbles. you're no longer authorized to seem into the bag. I enable you understand it is composed of all white marbles. You attain in and pull one out. that is black. What do you understand?? properly, you understand I’m a liar. (With a attractiveness like “Tony” wot do youse assume?) O.ok., now which you’ve “caught me”, I enable you understand. “properly, honestly, there is one black marble in the bag and 9 white ones.” You replace the marble you took out, attain in, and pull out a(nother?) black marble. What do you understand? properly, that is not likely you may pull out 2 black marbles in a row if the threat is a million/10 on each and each attempt. With 2 tries, you have a a million/one hundred danger of doing that. Is it available? particular. then you definitely attain in and pull out yet another black marble. NOW you have a determination to make. Do you call me a liar or no longer?? in case you call me a liar and there is in fact basically one black marble in the bag, you have made an blunders (and harm my thoughts). on the different hand, in case you say, “properly, it would desire to be genuine” and that is not genuine, then you rather've additionally made an blunders. the 1st blunders is termed a “type I” or “alpha” blunders; the 2d is termed a “type II” or Beta blunders. this is the essence of “hypothesis attempting out”. We take a pattern from some inhabitants and compute some statistic on it (e.g. recommend). We make some hypothesis approximately what that huge type ought to appear like based upon some concept or suggestions. We then compute how possibly (threat--root be conscious probable) that effect is that if in fact our unique supposition is right. usually, in maximum situations, we decide for .05 through fact the “value point” in that if the effect we be conscious might ensue under 5 situations in one hundred, we can end that our unique hypothesis is incorrect (reject the “null” hypothesis). Now, on your difficulty. Ho: the % = 88 H1: the % <> 88 You do the test by way of identifying on a definite variety of adults. in fact, the % IS 88%, yet your pattern is such which you end that that is unequal to 88. this is a variety I (alpha) blunders. You do the test by way of identifying on a definite variety of adults. in fact, the % isn't 88%, yet do to sampling blunders or loss of capability or undesirable luck, you end that that is 88% (or, to be greater precise, you end which you haven't any longer any reason to have confidence that is not 88%) this is a variety II (beta/capability) blunders. consistently, tony

Answer 3

permit’s initiate from scratch. I even have right here a bag of marbles. you're no longer approved to look into the bag. I permit you be attentive to it includes all white marbles. You attain in and pull one out. it is black. What do you be attentive to?? properly, you be attentive to I’m a liar. (With a recognition like “Tony” wot do youse assume?) O.ok., now which you’ve “caught me”, I permit you be attentive to. “properly, easily, there is one black marble interior the bag and 9 white ones.” You replace the marble you took out, attain in, and pull out a(nother?) black marble. What do you be attentive to? properly, that is not likely you will pull out 2 black marbles in a row if the possibility is a million/10 on each and every attempt. With 2 tries, you have a a million/one hundred probability of doing that. Is it achieveable? particular. then you definately attain in and pull out yet another black marble. NOW you have a determination to make. Do you call me a liar or no longer?? in case you call me a liar and there is in certainty basically one black marble interior the bag, you have made an errors (and harm my thoughts). on the different hand, in case you're saying, “properly, it must be authentic” and that is not authentic, then you somewhat've additionally made an errors. the 1st errors is noted as a “type I” or “alpha” errors; the 2nd is noted as a “type II” or Beta errors. it somewhat is the essence of “hypothesis finding out”. We take a pattern from some inhabitants and compute some statistic on it (e.g. advise). We make some hypothesis approximately what that type ought to look like based upon some theory or information. We then compute how probable (danger--root observe in all probability) that result's that if in certainty our unique supposition is authentic. usually, in maximum circumstances, we choose .05 because of the fact the “value point” in that if the end result we be conscious would take place below 5 circumstances in one hundred, we are able to end that our unique hypothesis is misguided (reject the “null” hypothesis). Now, on your difficulty. Ho: the % = 88 H1: the % <> 88 You do the test by choosing a definite type of adults. in certainty, the % IS 88%, yet your pattern is such which you end that it is unequal to 88. it somewhat is a type I (alpha) errors. You do the test by choosing a definite type of adults. in certainty, the % isn't 88%, yet do to sampling errors or loss of capacity or undesirable success, you end that it is 88% (or, to be extra precise, you end which you haven't any longer have been given any reason to have self assurance that is not 88%) it somewhat is a type II (beta/capacity) errors. constantly, tony