Why do we need to use degrees of freedom with the t distribution, but not the...

Why do we need to use degrees of freedom with the t distribution, but not the z distribution?

Expert Solution

t-distribution is a type of sampling distribution which depend on the sample size. As we know Z distribution is applicable for large sample test i.e if sample size, n>30 then we use Z-test and the value of Z i.e. area of the standard normal curve doesn't depend upon the value of n, it only depends upon the α. But the value of t i.e. area of the t-distribution depends upon the value of n and α both and it is applicable whenever sample size, n≤ 30.

Basically, degree of freedom= sample size - 1 or total no. of data- no. of conditions

For example, the critical value of t at 15 degrees of freedom at α= 0.05 is 2.13 and if there is 18 degree of freedom, then the value of t at α= 0.05 is 2.10. But the critical value of Z at 0.05 level of significance is 1.96 and at 0.10 level of significance is 1.645, it doesn't matter the size of the sample.

That's why we need to use degrees of freedom with the t distribution, but not the z distribution.

orchestra answered 2 years ago

Find the value of t for a t-distribution with 3 degrees of freedom such that the...

Find the value of t for a t-distribution with 3 degrees of freedom such that the area to the left of t equals 0.10. Possible Answers: A. 5.841 B. 4.541 C. -2.333 D. -1.638

State the total degrees of freedom for the following t-tests. (If you need to use ∞,...

State the total degrees of freedom for the following t-tests. (If you need to use ∞, enter INFINITY.) (a) n = 14 for a one-independent sample t-test (b) df1 = 15, n2 = 25 for a two-independent sample t-test (c) critical value = 63.657 for a two-tailed test, α = 0.01 (d) critical value = 1.645 for a one-tailed test, α = 0.05

As the degrees of freedom increase, the t distribution approaches the z distribution. Explain.

Find the critical value of t for a t-distribution with 30 degrees of freedom such that...

Find the critical value of t for a t-distribution with 30 degrees of freedom such that the area between -t and t is 99% A student records the repair costs for 25 randomly selected computers from a local repair shop where he works. A sample mean of $216.53 and standard deviation of $15.86 are subsequently computed. Assume that the population distribution is approximately normal and s is unknown. Determine the 98% confidence interval for the mean repair cost for all...

Consider the t-distribution with 18 degrees of freedom. Use Table D to find the proportion of...

Consider the t-distribution with 18 degrees of freedom. Use Table D to find the proportion of this distribution that lies below t=−1.33 Then use excel to confirm your result. Give your answer to two decimal places. P(t < −1.33) =

For a t-distribution with 15 degrees of freedom, 90% of the distribution is within how many...

For a t-distribution with 15 degrees of freedom, 90% of the distribution is within how many standard deviations of the mean? Select one: a. 1.235 b. 1.576 c. 1.753 d. 1.960

How does a t-distribution differ from the z-distribution? How do degrees of freedom (df) affect this?...

How does a t-distribution differ from the z-distribution? How do degrees of freedom (df) affect this? What is the effect of this difference on hypothesis testing? - Your friend performed a two-tailed experiment in which n = 20. He couldn’t find his t-table, but remembered the t-critical at df = 10. He decided to compare his t-obtained to this t-critical and determined the results were not significant. Is this ok? Why or why not.

What happens to a Student's t-distribution as the degrees of freedom increase? a.A student's t-distribution diverges...

What happens to a Student's t-distribution as the degrees of freedom increase? a.A student's t-distribution diverges from the standard normal distribution as the degrees of freedom increases b.A student's t-distribution converges to the standard normal distribution as the degrees of freedom increases

What is t distribution and how it is related to degrees of freedom? How is z...

What is t distribution and how it is related to degrees of freedom? How is z distribution different from t distribution?

Consider a random variable T that has a t-distribution with k = 16 degrees of freedom....

Consider a random variable T that has a t-distribution with k = 16 degrees of freedom. What is P(T > 1.8)? Group of answer choices 0.0454 0.9546 0.2499 0.4742 0.8000

Question