Question

find the 90th percentile of a t-distribution with a sample size n of 15​

Answer 1

Answer:

Step-by-step explanation:

When you want to find percentiles for a t-distribution you can use the t-table. A percentile is a number on a statistical distribution whose less-than probability is the given percentage, for example, the 95th percentile of the t-distribution with ,n – 1 degrees of freedom is that value of whose left-tail (less-than) probability is 0.95 (and whose right-tail probability is 0.05).

The t-table shows ,right-tail probabilities for selected t-distributions. You can use it to solve the following problems.

Suppose ,you have a sample of size 10 and you want to find the 95th percentile of its corresponding t-distribution. You have n – 1= 9 degrees of freedom, so, using the t-table, you look at the row for df = 9. The 95th percentile is the number where 95% of the values lie below it and 5% lie above it, so you want the right-tail area to be 0.05. Move across the row find the column for 0.05, and you get

This is the 95th , percentile of the t-distribution with 9 degrees of freedom.

Now if you increase the sample size to n = 20, the value of the 95th percentile decreases look at the row for 20 – 1 = 19 degrees of freedom, and in the column for 0.05 (a right-tail probability of 0.05) you find degrees of freedom indicate a smaller standard deviation and thus, the t-values are more concentrated about the mean so you reach the 95th percentile with a value of t closer to 0.

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