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The population has a mean of $25$and a standard deviation of $5$. According to the data, the population has a mean of $25$and a standard deviation of $5$. The sample size is $108$people, and the sample mean is $24$. Now, for a hypothesis test.

Typically, a hypothesis test is conducted on a sample of data drawn from a broader population. This test is used to generate results from sample data based on a hypothesis. Because we have the standard mean, standard deviation, sample mean, and population size, the hypothesis test may be performed using the normal distribution approach. The normal distribution is a continuous probability distribution with a bell shape in which all values cluster around the mean.

We must use the following formula to calculate using the normal distribution:

The sample mean is $\overline{X}$, the population mean is $\mathrm{μ}$, the standard deviation is $\mathrm{σ}$, and the sample size is $\mathrm{η}$.

$Z=\frac{\stackrel{¯}{X}}{\mathrm{σ}}\frac{-\mathrm{μ}}{/\sqrt{\mathrm{η}}}$

$\frac{24-25}{5/\sqrt{108}}$

$$\begin{gathered} =\frac{-1}{5/10.3923} \\ =-2.078 \end{gathered}$$

As a result, the normal distribution approach is suitable for larger populations with established standard deviation values.