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=

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

Using the inverse t-distribution function:

\[
c \approx -1.734
\]

Thus, \( c \approx -1.734 \).

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 \( P(t \leq c) \) 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.

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=

This guide explains how to find the t-value corresponding to P(t <= c) = 0.05 for a t-distribution with 18 degrees of freedom. The solution uses the inverse t-distribution function and is ideal for college-level statistics students.

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