You can use both the t statistic and the z statistic to test hypotheses about th

Question

You can use both the t statistic and the z statistic to test hypotheses about the mean of a population. The test that uses the t statistic is typically referred to as a t test, while the test that uses the z statistic commonly called a z test. Which of the following statements are true of the t statistic? Check all that apply. The t statistic provides an increasingly bad estimate of z at increasingly large sample sizes. When you do not know the population standard deviation, you can use the t-statistics, assuming all relevant assumptions are satisfied. The formula for the t statistic is t = (M - p)/ The numerator of the t statistic is different than the numerator of the z statistic. With the exception of whether the population standard deviation is known, the necessary assumptions for hypothesis tests with the t statistic and with the z statistic are _______.

Explanation / Answer

Option B and C are correct. When we don't know the population standard deviation, we can use t test and use sample standard deviation , assuming all other assumptions are satisfied like population is normally distributed.

Also, Formula is same as z formula , except we use sample standard deviation in the denominator

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