Math Problem Statement
consider a t distribution with 18 degrees of freedom. Find the value of c such that P(t<=c)=0.05. round your answer to at least three decimal places. c=
Solution
To find the value of such that for a t-distribution with 18 degrees of freedom, we need to look for the t-value that corresponds to a cumulative probability of 0.05 in the left tail of the t-distribution.
This can be obtained using a t-distribution table or a statistical calculator. We are looking for the value of such that the cumulative probability up to is 0.05, with 18 degrees of freedom.
Using the inverse t-distribution function:
Thus, .
Would you like any further details or have additional questions?
Here are some related questions to consider:
- How does the t-distribution differ from the normal distribution?
- What is the significance of degrees of freedom in a t-distribution?
- Why is the t-distribution used for small sample sizes?
- How would you find for other cumulative probabilities?
- What is the t-distribution used for in hypothesis testing?
Tip: In a t-distribution, as the degrees of freedom increase, the distribution approaches a normal distribution.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Statistics
t-Distribution
Cumulative Probability
Formulas
Inverse t-distribution function
Theorems
t-distribution properties
Cumulative probability in a t-distribution
Suitable Grade Level
College-level Statistics