# With alpha = .05 and df = 8, the critical values for a two-tailed t test are t = +-2.306. Assuming all other factors are held constant, if the df valu

With $\alpha =.05$ and df = 8, the critical values for a two-tailed t test are $t=±2.306$. Assuming all other factors are held constant, if the df value were increased to df = 20, what would happen to the critical values for t?
a. They would increase (move farther from zero).
b. They would decrease (move closer to zero).
c. They would stay the same.
d. Not enough information to answer
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cyhuddwyr9
Step 1
Density curves of the t distribution are similar in shape to the normal distribution curve. The t distributions have more observations in the tails and less in the center than the normal distributions. As the degree of freedom increases, the t-distribution approaches the standard normal distribution. The standard normal distribution has mean 0. Thus, if all the other factors are held constant, and the df value were increased to 20, the critical values for t would decrease and will get move closer to mean, i.e., will get close to zero.
Step 2
Correct option:
b.They would decrease (move closer to zero).