I'm glad to be of help.

HELP?

I'm glad to be of help!

I'm glad to be of help. The difference is often small, but I don't think that's a valid reason to have that error in there :)

I'm not sure what you mean by "the sample size required for the hypothesis test". Conceivably we could carry out a hypothesis test on a mean with a sample size of 1 (if we knew the population variance sigma^2.) If you're asking about calculating the sample size to achieve a given power of the test, then I don't have a video that looks at that directly. (I have videos that look at the relationship between sample size and power, and I have a video outlining how to calculate the sample size for a given margin of error for a confidence interval.)

jbstatistics i got the whole picture now , thank u for ur reply

You are very welcome!

As a general rule I don't use the rejection region approach, even when carrying out a test at a fixed significance level. I think that since the p-value approach leads to the exact same conclusion at a fixed significance level, but gives you the p-value, and the p-value is typically reported by software, that's the better path. Here I was illustrating the difference between t and z tests, in inference for the mean of a normally distributed population. I wasn't getting into the details of hypothesis testing beyond that. It was a fabricated example to show there can be meaningful differences between the t and z, even when the sample size is not all that small. But to address the big picture idea of what you're asking here, in the vast majority of hypothesis testing scenarios no actual decision is being made. Sometimes there is, and if a decision is being made solely on the results of the test (e.g. tossing an explanatory variable out of a multiple regression model in a backwards elimination procedure, say), and so then we need a rule. In the vast majority of cases, no actual decision is being made, and I think it simply doesn't make sense to impose an arbitrary decision rule in spots where no decision is being made. Imposing a binary decision on what is in reality a continuum , where no binary decision is necessary or needed, is not the way to go. Under the assumptions of the test in this video, if H_0 is true then the p-value has a uniform distribution on (0,1). We'd see a p-value of 0.568 or smaller more than half the time if the null is true, so there's no evidence whatsoever against H_0. There doesn't need to be an arbitrary decision rule to come to that conclusion. Much of this is opinion, and we could debate the nuances of hypothesis testing for the next century, as has been done for 1+ centuries. But I'm pretty sure that on my deathbed I'll still think that's a crime against science that everybody got fixated on acting like we're making a reject/don't reject H_0 decision at 0.05 as the default way to go about things.

@jbstatistics I appreciate you taking the time to explain that to me. What a selfless character you have! Respect! I believe that, just like your other videos, this explanation will help many people, not just myself. Thank you again, and keep up the wonderful work! 👏

@@BNT05 Thanks for the kind words! I may not be selfless, but I do truly want to help people learn :)

@@jbstatistics And you manage to do magnificently, imo: 😊

I agree. If your sample is large (~1000) just go with z

I feel that I do address this in detail in this video. Starting at around 2:20, I explain that some sources use the n > 30 rule, I say that I don't agree with this approach, and then I illustrate why I feel it's not a great approach. Was there some specific part of that discussion that you weren't following or found confusing?

nope, got you right, does that mean if i use a z test id still arrive at the same answer....im asking cos i have exams tomorrow, hoping you re not offended by my request

If you're trying to get the highest mark on a test, do whatever your professor tells you to do. I don't know how your prof designs tests, or what he or she considers right or wrong. The reality of the situation is that if you use a z test when you should be using t, even for a larger sample size, then the p-value you find will be a little off. Cheers.

You are very welcome Scott! As you can probably tell from how I phrase it in this video, the "n > 30" thing that many focus on makes me angry/sad. Cheers.

The entire purpose of this video was to discuss that. That's what this video is about. I have a detailed discussion about it here. Then I say the decision shouldn't be based on sample size. It should be based on the notion that I discuss in the video (whether the population standard deviation is known (almost never), or whether it is estimated from sample data (almost always)).

I apologize I guess I didn't catch that in the video. How can we determine whether to use z-statistic or t-statistic if it isnʼt clearly stated in a question what the population standard deviation is?

@@irafundafunda2898 In my videos I discuss the reality of the situation, and not various ways of answering questions depending on the wording. How best to answer a question depends on its precise wording, and also the beliefs of the questioner and grader. All that said, your question doesn't make sense and is not answerable as stated. If you mean instead "how would we tell if the standard deviation given in a question is from the population or from the sample?" then that depends on the wording of the question and on the beliefs of the person who wrote it.

@@jbstatisticsOkay I see.

+Dave Pennock The sample standard deviation can be calculated from sample data. If there is no sample data, then you wouldn't have any information and you couldn't carry out a test.

Kelsea T no

HELP

Too many jargons but i got it with repetition and other similar videos.