Calculates the pvalue of the statistical test for the population mean.
Syntax
TEST_MEAN(x, mean, Return_type, Alpha)
x is the input data sample (one/two dimensional array of cells (e.g. rows or columns))
mean is the assumed population mean. If missing, the default value of zero is assumed.
Return_type is a switch to select the return output (1 = PValue (default), 2 = Test Stats, 3 = Critical Value.
Method  Description 

1  PValue 
2  Test Statistics (e.g. Zscore) 
3  Critical Value 
Alpha is the statistical significance of the test (i.e. alpha). If missing or omitted, an alpha value of 5% is assumed.
Remarks
 The sample data may include missing values (e.g. #N/A).
 The test hypothesis for the population mean:
$$H_{o}: \mu=\mu_o$$
$$H_{1}: \mu\neq \mu_o$$
Where:
 $H_{o}$ is the null hypothesis.
 $H_{1}$ is the alternate hypothesis.
 $\mu_o$ is the assumed population mean.
 $\mu$ is the actual population mean.
 For the case in which the underlying population distribution is normal, the sample mean/average has a Student's t with T1 degrees of freedom sampling distribution:
$$\bar x \sim t_{\nu=T1}(\mu,\frac{S^2}{T}) $$
Where:
 $\bar x$ is the sample average.
 $\mu$ is the population mean/average.
 $S$ is the sample standard deviation.
$$ S^2 = \frac{\sum_{i=1}^T(x_i\bar x)^2}{T1}$$  $T$ is the number of nonmissing values in the data sample.
 $t_{\nu}()$ is the Student's tDistribution.
 $\nu$ is the degrees of freedom of the Student's tDistribution.
 The Student's tTest for the population mean can be used for small and for large data samples.
 This is a twosides (i.e. twotails) test, so the computed pvalue should be compared with half of the significance level ($\alpha/2$).
 The underlying population distribution is assumed normal (gaussian).
Examples
Example 1:


Formula  Description (Result)  

=AVERAGE($B$2:$B$11)  Sample mean (0.0256)  
=TEST_MEAN($B$2:$B$11,0)  pvalue of the test (0.472) 
Files Examples
References
 George Casella; Statistical Inference; Thomson Press (India) Ltd; (Dec 01, 2008), ISBN: 8131503941
 K.L. Lange, R.J.A. Little and J.M.G. Taylor. "Robust Statistical Modeling Using the t Distribution." Journal of the American Statistical Association 84, 881896, 1989
 Hurst, Simon, The Characteristic Function of the Studentt Distribution , Financial Mathematics Research Report No. FMRR00695, Statistics Research Report No. SRR04495
Comments
Article is closed for comments.