Section 7-4. Estimating a Population Mean: σ Not Known. ASSUMPTIONS: σ NOT KNOWN. 1. The sample is a simple random sample. 2. Either the sample is from a normally distributed population or n > 30. When σ is not known we will use the Student t Distribution.
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Estimating a Population Mean:
σ Not Known
1. The sample is a simple random sample.
2. Either the sample is from a normally distributed population or n > 30.
When σ is not known we will use the Student t Distribution.
If the distribution of a population is essentially normal, then the distribution of
is essentially a Student t distributionfor all samples of size n, and is used to find critical values denoted by tα/2. The Student t distribution is often referred to as the t distribution.
Degrees of Freedom (df) corresponds to the number of sample values that can vary after certain restrictions have been imposed on all data values.
In this section,
degrees of freedom = n− 1
where (1 −α) is the confidence level andtα/2 has n − 1 degrees of freedom.
NOTE: The values for tα/2 are found in Table A3 which is found on page 606, inside the back cover, and on the Formulas and Tables card.
Point estimate of µ:
Margin of error: