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 cc such that P(tc)=0.05P(t \leq c) = 0.05 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 tt such that the cumulative probability up to tt is 0.05, with 18 degrees of freedom.

Using the inverse t-distribution function:

c1.734c \approx -1.734

Thus, c1.734c \approx -1.734.

Would you like any further details or have additional questions?

Here are some related questions to consider:

  1. How does the t-distribution differ from the normal distribution?
  2. What is the significance of degrees of freedom in a t-distribution?
  3. Why is the t-distribution used for small sample sizes?
  4. How would you find P(tc)P(t \leq c) for other cumulative probabilities?
  5. 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.

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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

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