Question

Describe the difference between a one tailed and a two tailed test. What is the difference between a z test and a t test, and how do you determine which one to use? Also, discuss when a two sample test would be used, and provide an example.

Answer 1

ANS::

as per given data

Describe the difference between a one tailed and a two tailed test.

A one tailed test cares about which side of the hypothesized parameter is the true parameter. Is it less than or greater than the hypothesized value?

The two tailed test simply wants to know if it is equal to the hypothesized value or not, regardless if it is greater or less than the hypothesized value.

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What is the difference between a z test and a t test, and how do you determine which one to use?

A t test is an approximation to the z test when we have a limited sample size and we do not know the population standard deviation. The t test uses t distribution, while z test uses z distirbution. A t test cares about the degrees of freedom, while z test does not.

We can use t test at all times, but it could be inconvenient solving for the degrees of freedom everytime. Hence, at times, some use z distribution if the sample size is large enough, say n > 30. We can also use z test when it is given that the values are normally distributed.

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Also, discuss when a two sample test would be used, and provide an example.

If we have two independent groups and we want to compare their means, we can do a two sample t test.

For example, if we want to compare the heights of 10-year-old male US students to the female US students of the same age, we can gather 2 independent samples and conduct the two sample t test.

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