When conducting a hypothesis test for the population mean, you will not know the population standard deviation, so you will have to use the sample standard deviation instead. How will this affect the process?

Jonas Huff

Jonas Huff

Answered question

2022-11-03

When conducting a hypothesis test for the population mean, you will not know the population standard deviation, so you will have to use the sample standard deviation instead. How will this affect the process?

Answer & Explanation

Justin Blake

Justin Blake

Beginner2022-11-04Added 11 answers

When we are conducting the hypothesis test for the population mean µ and we know the population standard deviation then we use the Z test -statistic to test the hypothesis. That will follow the normal distribution.
z = x ¯ μ σ / n μ :  populatiom mean σ :  population standard deviation
But when we don't know the population standard deviation, we have to use sample standard deviation instead of population standard deviation. Then the test statistic follows the t-distribution with (n-1) degrees of freedom instead of normal distribution.
z = x ¯ μ S / n t ( n 1 ) , a / 2 S :  sample standard deviation

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