Timeline for Why do we compute the standard deviation of the proportion using the value assumed under the null hypothesis?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Jul 4 at 4:38 | vote | accept | inhjop | ||
| Jul 4 at 4:04 | history | edited | User1865345 |
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| Jul 4 at 3:53 | answer | added | User1865345 | timeline score: 2 | |
| Jul 4 at 2:01 | comment | added | inhjop | Thanks Alexis. I think, my questions is whether we should use p from null hypothesis or alternative hypothesis to compute type II error (in my example in the screenshot from the text, H0: p = 0.92 while Ha: p = 0.92). IIUC, we primarily use the STDEV under the null hypothesis to determine the critical values. Then, we use the standard deviation under the alternative hypothesis to calculate the probability that the test statistic falls within the non-rejection region when the alternative hypothesis is true (i.e. we want to use Ha: p = 0.90 to compute 𝜎 instead of H0: p = 0.92) for β. | |
| Jul 3 at 18:51 | comment | added | Alexis | $\sigma$ is purely a function of/is not independent of $\mu$ (aka $p$) when dealing with proportions. Assuming $\text{H}_0$ is true (which is part of null hypothesis testing's logic), then $\sigma = \sqrt{p(1-p)}$ by definition. | |
| Jul 3 at 16:21 | history | edited | inhjop | CC BY-SA 4.0 |
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| Jul 3 at 16:08 | vote | accept | inhjop | ||
| Jul 3 at 23:06 | |||||
| Jul 3 at 4:47 | comment | added | inhjop | re:Would I make my comment an answer if you wish? – Yes, please :)! | |
| Jul 3 at 4:46 | comment | added | inhjop | What if we don't know 𝜎 then we have to compute it using the value assumed under the null hypothesis? | |
| Jul 3 at 4:43 | comment | added | inhjop | Apologize, you are right. 𝜎 is defined as 21 in the video. That makes sense. | |
| Jul 3 at 4:35 | comment | added | User1865345 | The test is re $\mu$ assuming $\sigma$ is known. The latter was taken to be $21.$ | |
| Jul 3 at 4:30 | comment | added | inhjop | In the video (6.55 min): I wonder how did the author conclude while calculating probability of type 2 error that 𝜎 is 21 even for the population with a μ of 43. | |
| Jul 3 at 4:04 | comment | added | User1865345 | In the video you linked, $\sigma$ is already given there and thus they are computing the z score. Could you clarify what you are asking? | |
| S Jul 3 at 0:31 | review | First questions | |||
| Jul 3 at 1:59 | |||||
| S Jul 3 at 0:31 | history | asked | inhjop | CC BY-SA 4.0 |