Testing the mean of a sample by the t-test and using a normal distribution
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Summary of testing the mean of a sample drawn from a normal distribution using a t&-test and
[Equation goes here &- download the original to see it.] [Equation goes here &- download the original to see it.] The graphs comparing Student&'s t to the standardised z indicates a further complication with the application of this test. As the sample size increases the estimation of the population variance improves. In other words, as n increases Student&'s t converges on the standardised normal distribution. [Equation goes here &- download the original to see it.] Thus, the difference between the t&-test and the z&-test diminishes as n gets larger. What this means is that the critical values of the t&-test depend on the sample size of n. Furthermore, since the t distribution is used primarily in the context of hypothesis testing, full t&-tables for each value of n are not usually given. Instead, critical values of the t&-test for each significance or probability level are quoted. Finally, the critical values are not cited for the sample size, n, themselves but for the number of degrees of freedom, , where [Equation goes here &- download the original to see it.] Degrees of freedom = sample size - 1 The table for the Student&'s t&-distribution commences as follow. [Table goes here &- download the original to see it.]
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Contents of
Testing the mean of a sample by the t-test and using a normal distribution
1 Testing the mean of a sample drawn from a normal distribution using a t&-test and using a no
2 Summary of testing the mean of a sample drawn from a normal distribution using a t&-test and
3 Example of testing the mean of a sample drawn from a normal distribution using a t&-test and
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