Question

1 and 2 please

1. Explain why you would conduct a t test rather than a z test. In other words, what is the difference between a one sample t test and a one sample z test? 2. Because of what is discussed in question 1, some of the components of calculating at value are different from the components of a z value. Specifically, the t value utilizes degrees of freedom. Explain what degrees of freedom means (you can include a demonstration if it helps).

Answer 1

1) Z-tests are a statistical technique that is used to compare population means to a sample's. The z-score tells you how far, in standard deviations, a data point is from the mean or average of a data set. Z-test is using in the problem where the sample size is greater than 30 and variance is known. Whereas t-test is used in the situation where the above conditions are not fulfilled.

You must use the t-distribution table when working problems when the population variance is not known and the sample size is small (n<30) otherwise t-test works the same as z-test. In some cases, experts use the z-test where population variance is not known but the sample size is greater than 30. Usually, t-tests are most appropriate when dealing with problems with a limited sample size (n < 30).

Do you know the population standard deviation, o.? Yes No Use the t-score Is the sample size above 30? Yes No Use the Z-score Use the t-score *Replaces in the t-score formula with

2) Degree of Freedom: Degrees of freedom of an estimate is the number of independent pieces of information that went into calculating the estimate.

The degree of freedom depends on how much data you have and how many parameters you are estimating. When you estimate a parameter it loses a degree of freedom.

Example: Suppose you have three numbers and you say that the average of the numbers is 10 then it means you can choose only two values freely after that the third value is automatically decided. This is an example of df that estimating a mean reduces the degree of freedom. It reduces the number of ways to choose observation independently.

Critical Values Decrease While DF Increase.

Here the critical value of t-statistic depends upon the degree of freedom, as the df gets higher, the area in the tails of the distribution gets smaller. As df approaches infinity, the t-distribution will look like a normal distribution. When this happens, you can be certain of your standard deviation (which is 1 on a normal distribution).