To find the t-value such that the area to the left of it is 0.02 with 17 degrees of freedom, you use a t-distribution table or a statistical calculator.

Steps:

1. Understand the symmetry hint: Since the t-distribution is symmetric, finding the left-tail area of 0.02 is equivalent to finding the t-value with area 0.98 to the right (or 0.02 in the left tail).

2. Use a t-distribution calculator or table:

   • Look up the critical t-value for a one-tailed test with 17 degrees of freedom and a significance level of $\alpha = 0.02$.

Using a calculator or table:

For $df = 17$ and left-tail area $0.02$: $t = -2.110$

Final Answer:

$t = -2.110$

Would you like a more detailed explanation or a demonstration using specific tools?

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Related Questions:

1. How do degrees of freedom affect the t-distribution?
2. Why is the t-distribution used instead of the normal distribution for smaller sample sizes?
3. How do you calculate a t-value using software like Excel or Python?
4. What is the interpretation of a left-tailed vs. a right-tailed t-test?
5. Can you explain the symmetry property of the t-distribution in more detail?

Tip:

When solving t-distribution problems, always verify whether the problem is one-tailed or two-tailed—it significantly affects the critical values.