Question

In your own words, explain the difference between a t statistic and a z score and include how the t distribution is related to the normal distribution.

Answer #1

The t test statistic is used in the test, when we are not sure that the distribution is normal and also the sample size is small so that the Central limit theorem cannot be applied.

The only difference between the t statistic and the z score is that t statistic is computed by assuming that the underlying data distribution is t distribution while z score for underlying distribution to be normal.

The t distribution is very similar to the normal distribution in the sense that it is symmetric about the mean. But there are some differences as well. The t distribution has fatter tailes and higher peakedness at the center of the distribution which means that the proportion of values lying away from the mean is greater as well as near the mean are greater in case of the t distribution.

In your own words, tell me the difference between using the z
test and the t test for testing the difference between 2 means.

P_1
Which of the following is a fundamental difference between the t
statistic and a z-score?
A. The t statistic uses the sample mean in place of the
population mean.
B. The t statistic computes the standard error by dividing the
standard deviation by n - 1 instead of dividing by n.
C. The t statistic computes the standard error using a sample
variance in place of the population variance.
D. All of these are differences between t and z...

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1. Which of the following is a major difference between a
hypothesis test with a t statistic and the test with a z-score?
a.
You must know the population standard deviation for the z-score
but not for the t statistic.
b.
You use the normal distribution table to find critical values
for t but not for z.
c.
You must know the population median for the z-score but not for
the t statistic.
d.
There are no major differences between...

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