Suppose you are lasting one population mean wilh 20 and Iha population normally disiribuied What test statistic should use?Approximale using Iho (iostUsa Ihe Sigu...

A population mean is 13. The sample mean is 12.8, and the sample standard deviation is two. The sample size is 20. What distribution should you use to perform a hypothesis test? Assume the underlying population is normal.

In 25. We have a population mean and a population center deviation. We also have a sample mean in a sample size. What distribution should you use in this one? Because the population center deviation is known, we're going to use a normal distribution that.

Problem 25 poking too. I didn't mind a degree of freedom. You're the population variance are equal. So degree of freedom equal to and more plus and two minus two If the population far variants are not equal. So the degree of freedom equal with the minimum off Anyone minus one and in the Tu minus one. Yeah, Then deter mined the critical values in table Find in every nxb and then you remind the corresponding the rejection region Then little mind the value off the test statistic so in the population are equal is equal toe one more When it's xto war over sigma square Root off one over and one cross one over and to yeah, eso sigma had is equal toe square root off in one in one minus one It's one is square waas in the tool when this one is two squared over in one plus any toe minus two in the population variance are not equal. So he is equally toe ex womb war minus Next to war over Square wrote off s one squared over in one is to square over in tow. If the value off the centrist etiquette within the rejection reasons to reject, the more he passes

We have a variable with a normal distribution and we want to find a confidence interval about the population means meal question want to answer is how do we find that confidence interval for the meal? Given a unknown sigma or unknown population standard deviation and be an unknown sigma or an unknown population standard deviation. So the question at hand is what distribution are we going to use? And each of these two scenarios for sigma known, we can automatically conclude that we're going to be using a normal distribution to find the Z score or standardized version of X bar, which we use to solve for and find the confidence interval next for signal unknown. We're going to note that we need a sample standard deviation s and as long as we have that sample standard deviation as to replace sigma, we can make use of a student's T distribution in order to derive this confidence interval.

The following is a solution to number one. And this asks about the conditions for inference that must be met whenever you're testing um for the population, mean, you and there are two things to look for. The first thing is that you have independence in your samples independence and the main things you look for there, we need to have random sampling. Okay, So I should say it should say something with a random sample or randomly sampled. And also the sample size needs to be no more than 10% of the population size. So the small end, that's the sample size needs to be less than or equal to 10% of the big end, which is the population. Um that means that each especially without replacement. So whenever you you pull someone from the sample, it doesn't make a huge dent in the population. And the second thing we look for is that the sampling distribution of X bar is approximately normal. And there are two scenarios where that can happen. If it's pulled from a population that is normal, then the sample size can be, you know, whatever. But if the population is not normal, we don't know the distribution of the population then And needs to be at least 30. Okay, so either the population is normal or if it's not normal or we don't know, that sample size needs to be at least 30 and then it asks us when to use the normal model or the Z distribution and when to use the T. Distribution. And basically you're gonna use the z distribution when sigma is known. So if you know what the population standard deviation is, um then you can use the z distribution. But if you don't know what sigma is, then you have to use this t. Distribution. So whenever sigma is unknown, you'll need to use the T distribution.