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Determine if each of the following statements if true regardingthe properties of t-distributions and t proceduresA. t-distributions have higher variation than the s...

Question

Determine if each of the following statements if true regardingthe properties of t-distributions and t proceduresA. t-distributions have higher variation than the standardnormal distribution.B. t-distributions result in higher critical values andtherefore give wider confidence intervals then z-confidenceintervals.C. t-procedures should be used for large samples and knownpopulation standard deviation σ.

Determine if each of the following statements if true regarding the properties of t-distributions and t procedures A. t-distributions have higher variation than the standard normal distribution. B. t-distributions result in higher critical values and therefore give wider confidence intervals then z-confidence intervals. C. t-procedures should be used for large samples and known population standard deviation σ.



Answers

Determine which of the following are true and which are false. Then, in complete sentences, justify your answers.
a. When the sample size is large, the mean of $\overline{X}$ is approximately equal to the mean of $X .$
b. When the sample size is large, $\overline{X}$ is approximately normally distributed.
c. When the sample size is large, the standard deviation of $\overline{X}$ is approximately the same as the standard deviation of $X .$

We want to determine whether or not the following statements are true or false. A The length of a confidence interval can be found if you only know the margin of error. E to answer this question, let's remember an important definition for confidence intervals. That is, the confidence interval is defined as expire minus E is less than you as an expert Plus C. From analyzing this definition, we see that the length of a confidence interval is simply equal to two times the margin of error, which means that the length is simply half the margin of error, meaning that this statement is true. If you know eat, you can find the length of the confidence interval next to part B. You can be found if you only know the length of the confidence interval. This is again true. You simply have to length. See, the confidence interval itself can be found if you only know E. So that means you can define expo minus is less than you is less than X plus C. This is false because we don't know X bar, which is critical for that formula, what we mentioned. Finally, D The confidence interval itself can be found if you only know Ian X bar. This is true. Our formula for the conference interval about meal that we define the top left is just X bar plus or minus E.

We want to determine whether or not the following statements are true or false. First he can be found. That is the margin of error can be found if you only know the confidence level of the interval. So in this particular case, let's remember an important definition, margin error. E is equal to the critical value scores E associated with a defiant confidence level, times the population standard deviation sigma divided by the root and where N is the number of samples. If you have the confidence level, you know exactly what Z alpha over two is. However, in this particular problem we know that he depends on all three of these variables Z alpha over to sigma and end since we don't know sigma and and that means we don't have enough information to determine E, which means this is false. Next confidence level can be found if you only know E. So you can figure out the confidence level Alpha by simply finding what Z is equal to E route and over sigma. Again, we don't have any sigma here. So this sentiment is again false. Now see it can be found if you know the confidence level sigma and and these are the exact two variables were missing from part A. So now this is true. Finally, the confidence level can be found if you only know E, sigma and N. Again E and N sigma, or rather an in sigma. We're the only thing is missing from part B. So this is true.

The internal given between 25 30 is a 90% confidence interval estimate for the population means you we want to interpret what this finding suggests. That is What does it mean to say that an interval is a 90% confidence interval for a mean? You so remember that confidence intervals are going to estimate a population stat with some percent confidence. However, that percent confidence does not allude to whether or not new is in the individual interval after all new is either not in or in a confidence interval with probability one or zero. It's either there or it's not there. So the question is then, what is the confidence intervals confidence level actually estimating? So we know that the 90% then must allude to the fact that 90% of intervals built by these samples. So by samples of similar size are going to contain you. So where are percent confidence is whether or not this general type of sample for the given sample size Will contain you. That means we can interpret this interval to mean if 90 of confidence intervals are calculated from all possible samples of a given size me will be a 90 of the confidence intervals.


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