You are testing a claim and incorrectly use the normal sampling distribution instead of the t-sampling distribution. does this make it more or less likely to reject the null hypothesis? is this result the same no matter whether the test is left-tailed, right-tailed, or two-tailed? explain your reasoning.
(more likely) for degrees of freedom less than 30, tail of the curve are thicker for a (t-sampling) distribution. therefore, if you incorrectly use the standard normal distribution, the area under the curve at the tails will be (smaller) what it would be for the t-test, meaning the critical value will lie (closer) the mean.
is the result the same?
a) the result the same. in each case, the tail thickness does not affect the occasion of the critical value(s).
b) the result is the same. in each case, the tail thickness affects the location of the critical value(s).
c) the result is different. with a two-tailed case, the tail thickness does not affect the location of the critical values, however, in a left- and right-tailed case, the tail thickness does affect the location of the critical value.
d) the result is different. with a left- and right-tailed case, the tail thickness does not affect the occasion of the critical value, however, in a two-tailed case, the tail thickness does affect the location of the critical value.