1. When the t distribution is used in constructing a confidence interval based on a sample size of less than 30, what assumption must be made about the shape of the underlying population?

2. Why are the t values listed in the df 5 infinity row of the t distribution table identical to the z values that correspond to the same right-tail areas of the standard normal distribution? What does this indicate about the relationship between the t and standard normal distributions?

3. In using the t distribution table, what value of t would correspond to an upper-tail area of 0.025 for 19 degrees of freedom?

4. In using the t distribution table, what value of t would correspond to an upper-tail area of 0.10    for 28 degrees of freedom?

5. For df 5 25, determine the value of A that corre- sponds to each of the following probabilities:

a. P(t $ A) 5 0.025

b. P(t # A) 5 0.10

c. P(2A # t # A) 5 0.99