The t-test for one population mean

Answer

In testing a claim about one population mean, the T-test uses the t distribution as the sampling distribution of the test statistic. This test is used when:

i). the sample is random and independent

i) sample is selected from a normally distributed population  or the sample size is greater than 30

ii) and the population standard deviation is unknown

The formula for calculating the test statitsic is given a sample of size n, and sample mean $\overline{x}$, and sample standard deviation s,

$t=\frac{\overline{x}-\mu }{s/\sqrt{n}}$

where , $\mu$ is the claimed population mean.

The degrees of freedom is given by df=n-1

for this test, we use the t distribution tables to read the p-values and the critical values using (n-1) degrees of freedom  for decision making on the null hypothesis

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