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Wmaedealopt6 Of 15 (5 complete)Find the critical value t for the confidence level c = 0.98 and sample size n = 18.Click the icon to view the t-distribution table_(R...

Question

Wmaedealopt6 Of 15 (5 complete)Find the critical value t for the confidence level c = 0.98 and sample size n = 18.Click the icon to view the t-distribution table_(Round to the nearest thousandth as needed:)nplleEnter your answer In the answer box fe

Wmaedealo pt 6 Of 15 (5 complete) Find the critical value t for the confidence level c = 0.98 and sample size n = 18. Click the icon to view the t-distribution table_ (Round to the nearest thousandth as needed:) nplle Enter your answer In the answer box fe



Answers

Find the critical value $t_{c}$ for the level of confidence c and sample size $n.$ $$c=0.99, n=16$$

In this problem, you're being asked to find the critical T value for a given level of confidence and sample size end now first, just to recap the basic concepts. So for a distribution like this, we know that it follows something called a T distribution. And this is a distribution where T is given by explore minus mu over s over the square root of n and just some important things to keep in mind here, Um, in a t distribution, we have a shaped like this. We have a sheep, something like this. And we know that the mean the mood and the media are all equal to zero, and the U. T distribution is bell shaped and it's symmetric about the mean and the total area under this curve is equal to one. Now the tea distribution and its shape is determined by something called do You Degrees of freedom and the degrees of freedom, which are often given as d f are the number of free choices left. But after a sample statistics such as X bar, where the mean is calculated and the degrees of freedom, DF is equal to end minus one, which is the sample size minus one and based off the degrees of freedom, your graph will have slightly different shapes. So, for example, if this is a standard normal curve, um then something with a degree of freedom of to might look a bit like this, while something with a degree of freedom of five might look something like this. Now for a problem Number two, we are given that the confidence interval is 95 and the sample size is 12. Now, we know the degrees of freedom are equal to the sample size minus one. So this would be 11. And now you need to go refer to table five in appendix B of your textbook, which shows all of the T values for a given see confidence interval, level of confidence and given degree of freedom. And we can see from the chart that for this given 95.95 level of confidence and degree of freedom of 11, the TC value is 2.2

Problem. Number four degrees of freedom is equal to end minus one, which is equal to 15 minus one so is equal to 14. So giving a is equal to one minus. Opened 99 34 to operate or one and the value of X are square with opened 995 and agree to Freedom 14 is equal to 31.319 for the critical value. Uh oh X squared with or point or four or five and degrees of freedom equal toe 14 The critical value ableto four points or 75

In this problem, you're being asked to find the critical T value for a given level of confidence and sample size end now first, just to recap the basic concepts. So for a distribution like this, we know that it follows something called a T distribution. And this is a distribution where T is given by explore minus mu over s over the square root of n and just some important things to keep in mind here, Um, in a t distribution, we have a shaped like this. We have a sheep, something like this. And we know that the mean the mood and the media are all equal to zero, and the U. T distribution is bell shaped and it's symmetric about the mean and the total area under this curve is equal to one. Now the tea distribution and its shape is determined by something called do You Degrees of freedom and the degrees of freedom, which are often given as d f are the number of free choices left. But after a sample statistics such as X bar, where the mean is calculated and the degrees of freedom, DF is equal to end minus one, which is the sample size minus one and based off the degrees of freedom, your graph will have slightly different shapes. So, for example, if this is a standard normal curve, um then something with a degree of freedom of to might look a bit like this while something with a degree of freedom of five might look something like this for the specific question, we know that the level of confidence is 0.9, and we know the degrees of freedom aren't equal to end the sample size minus one. And since we know that thesis sample size in this problem is 10, then the degrees of freedom are equal to nine. Now, to do this problem, what you should do is refer to table five and appendix B of your textbook. And there you have a big chart correlating the confidence intervals and the degrees of freedom to the needed T value. So if you go look in your book, we can see that the T value, which is T value 0.9 with nine degrees of freedom according to the chart, is 1.83 And so that is your final answer

In this problem, we are given all the necessary details about a sample and we're being instructed to construct the indicated confidence interval for the population. Mean you using a T distribution. So just to recap in 80 distribution, Um, what we're working with is that we don't know what the population standard of Yushin Sigma is, and we have to work with the sample standard deviation which has given us s now in this problem were given that we want a 0.9 confidence level. So we want a 90% confidence interval. And we also are given that the mean of X X bar is equal to 12.5 and we're given that the sample standard deviation is 2.0. But once again, we don't know the population standard deviation and were given to the sample size. End is equal to six now to use it to you distribution. The first thing we need to do is find the T value TC And to do this, we need to find the degrees of freedom. And we also need to know the level of confidence So the degrees of freedom are equal to end minus one which is six minus one, which is equal to five. And we already know that the confidence level is 0.9. So given this information, we can go look at the table for in appendix B and we see that the T value for the sample is 2.15 Now, Since we don't know Sigma, we need to calculate the margin of error to find the confidence interval. And to do so were given the equation off. E equals t times as over the square root of n and we can plug in from the T value that we already know to get 2.15 times to the S value over the square root of six. And this is equal to approximately 1.65 Now. Finally, we can put this into our confidence interval, which is are mean, plus or minus our error. So we have 12.5, minus 1.65 which is equal to 10.84 and 12.5 plus 1.65 which is equal to 14.15 Thus, our confidence interval is between 10.84 and 14.15


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