The
problem is that if you calculate a sample mean and it is different from the one
hypothesized, there are** **two
possible reasons for the difference:

·
Your sample comes from a different population and the sample mean
represents a different population mean. When this happens, you reject the Null
Hypothesis.

·
The group comes from
the same population and the mean varies
by chance. You just happened to pick up such a sample. When this
happens, you did not reject the Null Hypothesis.

Using one sample t-test, comparing the
sample mean to the population mean, to get an estimate of the probability that
the sample mean is different by chance.

**Requirements:**

The variable should be ** normally
distributed**, which can be evaluated by looking at the distribution of
the data (via histograms, box plot, or QQ plot) or by performing a normality
test.

Below is the **sample
input window**

Below is the **sample
output and explanation** of the above model:

t test comparing sample
mean to populational mean

One Sample t-test

**(1)
T test for BMI comparison to true mean: 22**

data: BMI

t
= -7.3697, df = 657, p-value
= 5.158e-13

alternative
hypothesis: true mean is not equal to 22

**(2) ****Observed
mean and its 95% confidence interval**

95
percent confidence interval:

21.18059 21.52537

sample
estimates:

mean of x

21.35298

**Empower also
output following box plot to show the means and distribution.**