Is the z-test the same as the t-test but only used when we know the true...

Is the z-test the same as the t-test but only used when we know the true value of population mean's variance? But in practice, I'm assuming that the population mean's variance is never observed so I'm confused why we use the z-test. When will the z-test be helpful when the t-test is not if we never know the population mean's variance in real life? What are the other two differences between the two tests?

Expert Solution

The Z test is used when population variance is given , and T test is wised when sample variance is given.

Also if the sample size is less than 30 then a T distribution is most prefferable because as the sampel size increses from size 30 then the distribution approaches a normal distribution.

The P-value for Z test is calculated using Z table shown below but P-value is calculated using Confidence level and degree of freedom as well.

T-ditribution table

orchestra answered 2 years ago

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