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. Is the null hypothesis more or less likely to be​ rejected? Explain. Less likely; for degrees of freedom less than​ 30, the tail of the curve are thicker for a t-sampling distribution.​ Therefore, if you incorrectly use a standard normal sampling​ distribution, the area under the curve at the tails will be larger than what it would be for the​ t-test, meaning the critical​ value(s) will lie closer to the mean. Is the result the​ same? 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. The result is different. With a​ left- and​ right-tailed case, the tail thickness does not affect the location of the critical​ value, however, in a​ two-tailed case, the tail thickness does affect the location of the critical value. The result is the same. In each​ case, the tail thickness affects the location of the critical​ value(s). The result the same. In each​ case, the tail thickness does not affect the location of the critical​ value(s).

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Answer:

If the sample size is sufficiently large, we can use normal distribution even when we don't know about the population variance. Hence, there is no change in the decision about the null hypothesis, since the critical values are approximately same. It is same for whether it is left-tailed, right-tailed or two tailed.

if the sample size is small and we don't know about the population variance, in that case normally assumption is fail so we cannot use the normal sampling distribution, we use only the t-sampling distribution. in this if we use the normal sapling distribution there is a difference in the inference about the null hypothesis

More likely for degrees of freedom less than 30, the tail of the curve are thicker for a t-sampling distribution. Therefore, if you incorrectly use a standard normal sampling distribution, the area under the curve t the tail will be smaller than what it would be for the t-test meaning the critical values will lie closer to the mean.

The result is the same, in each case, the tail thickness affects the location of the critical value.

Step-by-step explanation: