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3.4 (2 points) What is the 99% confidence interval? Table 2:UWd)T D76728...

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3.4 (2 points) What is the 99% confidence interval? Table 2:UWd)T D76728

3.4 (2 points) What is the 99% confidence interval? Table 2: UWd) T D 76 728



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$t$ -models, part II Using the $t$ tables, software, or a calculator, estimate
a) the critical value of $t$ for a 95$\%$ confidence interval with df $=7 .$
b) the critical value of $t$ for a 99$\%$ confidence interval with df $=102$
c) the P-value for $t \leq 2.19$ with 41 degrees of freedom.
d) the P-value for $|t|>2.33$ with 12 degrees of freedom.

For this problem. We need to calculate the T statistic based on Ford or five different scenarios. So I've written down the 1st 1 so we can walk through it together. We have a sample size of 18 and we want the T statistic for a 99% confidence interval. The way we're going to do this is pretty simple. The first thing we're gonna do is calculate the degrees of freedom. Degrees of freedom, if you might recall, is calculated using n minus one. So for scenario, a are degrees of freedom are going to be 17. The next thing you're going to do is looking your textbook and flip to the table in the back of the book. Um, with the tea table, it should look something like this. You're gonna have degrees of freedom running down in a column on the left side, right here and then horizontally. You're gonna have different percentages for confidence intervals. So using this table, you'll find your degrees of freedom, which is 16. In this case, you'll find your confidence level, which is 99% for this scenario and your reader table to find the T value of interest which will be right there. Um, for this set up, your answer should be 2.898 Let's try be B tells us that we have a 23 sample size and a 95% confidence interval, so we'll calculate our degrees of freedom. With just 22 minus one. We'll find 22 on the degrees of Freedom Column will find 95 on the confidence interval Percentage column. Match the two up and your answer should be 2.74 was give see ago. See is an equals 15 with a 98% confidence interval. Find your degrees of freedom 14 and your answer is two point 6 to 4. Now I'll let you try D and E on your own. It's the same thing we've been doing up till now. And if we're doing it right, you should get 1.833 and 2.9 three

The following is a solution for # three. And we're asked to find a 980% confidence interval given this this data here. So we're gonna use the formula that I have up in red here, it's p one minus p two hats. In this case it's 20.255 -0.193 plus or minus Now the Z score here. If you don't have it memorized, that's fine. In fact, I can show you how to get it real quick because this one isn't as typical. So 1995-99 are usually the most typical ones. But if we go to distribution here and inverse norm And we type in .8 And then the center will be center is always for confidence intervals and then we paste, we get positive negative 1.282. So that's what we're gonna use for our z value. So positive, negative 1.282 times the square root of 0255 Times 1 -255. Which is 0.745 Divided by that sample size of 300 Plus 019, three Times 1- that. Which is 0807. And that's divided by the other sample size of 400 and you should get 0.062 plus or -0.041. So you can leave it like that. Or you can actually expand it out Where you subtract and you add you should get 0.021. Oops, Okay. All the way up to 0.103. Okay, so either answer is acceptable. Now we find a 95% confidence interval Given this following data. So we started out the same way now 95% confidence that we should know that Z value that's 196. But let's go and start this .1 47 which is the P one hat minus 10.131 Plus or -1.96 which is the critical value for 95 times the square root of .147 Times 1 -147 which is 853. And then divide that by the sample size of 3500 And then plus .131 Times 1 -131, which is 869. And divide that by the sample size of 37 50. So whenever you do that you should get .016 plus or minus .0159. So you can leave it like this certainly. Or you can expand it out groups Where you get essentially zero, also point 0001 All the way up to 0.0319. Okay, so those are two representations of the 95% confidence interval. Given this data

To this question. Simply a matter of reading the tea table. So for a If we look at our table, we get a value of two 0.2 to 8 for T star For B, we get 2.131 for C 2.947 Again, I'm just looking at the tea table, which is typically in the back of your textbook for D. You get an end value of five degrees of freedom of four and thus from that, you know that T star would be 4.60 four. We expand this outward for E. We get 2.492 for in we have our sample size of 38 or degrees of freedom of 37. Thus rt Star values 2.715

In this question in order to build a confidence interval. What are the steps that we would take? I see that there are only 17 salaries, which means that the sample size is less than 30. So we're definitely going to use a T distribution. In this case, Sigma is also not known so again, tea distribution. So find the critical value. P Alfa by two The option is correct. State no option is correct. In this case, this is our answer.


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