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In a one-sample t-test, what must be calculated to compute the critical value of t ?Confidence intervalsThe observed value of tDegrees of freedomThe mean of the sam...

Question

In a one-sample t-test, what must be calculated to compute the critical value of t ?Confidence intervalsThe observed value of tDegrees of freedomThe mean of the sample:

In a one-sample t-test, what must be calculated to compute the critical value of t ? Confidence intervals The observed value of t Degrees of freedom The mean of the sample:



Answers

If we use the sample data in Exercise 2 for constructing a $99 \%$ confidence interval, what is the number of degrees of freedom that should be used for finding the critical value of $t_{\alpha / 2}$ ? What is the critical value $t_{\alpha / 2} ?$

We want to determine the critical value for a two tailed hypothesis test of population name, you where the population standard deviation sigma is unknown at alpha equals 20.5 confidence with 12 degrees of freedom. This question is testing our understanding of hypothesis tests for population means knew where the standard deviation is unknown. In particular is testing an understanding of the student's T distribution, which is critical in conducting these types of tests. So let's first draw the scenario out to understand what we're looking for. To first and foremost we're looking for the plus or minus 10 on this is a two tailed tests, which splits the student's T distribution of degree freedom 12 into two tails area 20.25 each to do so, we're going to be using a tea table. That's what students distributions were defined T. Such that people 80 greater than or equal to the absolute value. Tina is 800.0 5/2 or 0.25 degree freedom 12 from the tea table. We obtained P. T. Greater than absolute value. Tina equals 120.25 occurs, for tina equals plus or minus 2.179

Okay, This is for number 57. We're looking for portable T value, which is Kurt Nolte star. So, for the question A, we have 10 observations. The in would be 10 and the confidence level that is given is, uh, 95% question be and equals two. There are 20 observations. An accomplice level would be 99%. So when I look at these two questions one after another and they're pretty similar, any questions? 10 on degrees of freedom in this case will be in minus one, which would be nine for the calmness level as 95%. We know the Alfa on wishes significance less, but it'll be 5% and 5% will be on the area of to tell us if you look out the Tekere. So 5% it will, referring to these hotels. So each of the tell would be 2.5% which is 0.2 So we're gonna use degrees of freedom being my and his point total. Five asked to write tell to determine our t start that you start could be obtained from the table beat. All right, so gonna look at the table B. All right, so here we go. We have the table B, and we're going to put into that we've got We're going to use the P, which is the right tail area and the degrees of freedom. All right, So the degrees of freedom, as we have said, is gonna be nine and the right tail, as we have calculates 0.0, to fight. So if you look at these two, refer to this table you can find the intersection number is the 2.262 But that is cortical a T value in this question in the party, So T star will be 2.62 to 2.262 is in the title, all right. Not caution be. And whose 20 we have degrees of freedom equals 2 19 Confidence level equals to 99%. So significance level alfa would be 1%. 1% is the same as point No one. So cutting to the T curve that were Guillain 11% of referring to the two tells and the right tail will be a point. No one to bother to. Butchers be porn. Oh, and we're gonna use this number of 0.2 Pope 0.5 as well as degrees of freedom equals 19 to the four hour T star by using the table Be. So let's turn to the table. Beat. All right, So question be we have degrees of freedom equals 2 19 and the right tail area is pointing over five. If you look at these two information, we're gonna find the intersection number in this table. Be as 2.861 messing me the cripple t in this case, 2.861 We have two point. Think that's what. All right, So that's form number of stone.

We want to determine the critical value for a right tail test. That is a hypothesis test of population. We knew where the standard deviation of the population sigma is unknown at 0.1 confidence and with 15 degrees of freedom, this question is testing our understanding of hypothesis tests for population. We knew what signal is unknown. In particular is testing our knowledge of the student's T distribution, which is critical to these types of tests. Let's first draw this out. We're looking for on a T distribution. The critical T score T not for which the area to the right is 150.1 Where the T distribution in question has degree of freedom. 15, putting this into words or equations were using a tea table to find T. Such that the probability T greater than thine own equals 150.1 with degree of freedom 15. Thus referring to a tea table for the students distribution and the appropriate degree of freedom, We find that the probability to us than Tina equals 150.99 The area left corresponds to a T, not of 2.602


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