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A sample of 300 subjects is tested for marihuana usage. Out of the 300 tested subjects, 27 of the results are wrong.

The null hypothesis is written as follows.

The proportion of results that arewrong is equal to 10%.

\({H_0}:p = 0.10\).

The alternative hypothesis is written as follows.

The proportion of results that arewrong is less than 10%.

\({H_1}:p < 0.10\).

The test is left-tailed.

The sample size is n=300.

The sample proportion of the results is computed below.

\[\begin{array}{c}\hat p = \frac{{{\rm{Number}}\;{\rm{of}}\;{\rm{results}}\;{\rm{that}}\;{\rm{were}}\;{\rm{wrong}}}}{{{\rm{Total}}\;{\rm{number}}\;{\rm{of}}\;{\rm{results}}\;}}\\ = \frac{{27}}{{300}}\\ = 0.09\end{array}\].

The population proportion of the results that are wrong is equal to 0.10.

The value of the test statistic is computed below.

\(\begin{array}{c}z = \frac{{\hat p - p}}{{\sqrt {\frac{{pq}}{n}} }}\\ = \frac{{0.09 - 0.10}}{{\sqrt {\frac{{0.10\left( {1 - 0.10} \right)}}{{300}}} }}\\ = - 0.577\end{array}\).

Thus, z=-0.577.

Referring to the standard normal table, the critical value of z at\(\alpha = 0.05\)for a left-tailed test is equal to -1.645.

Referring to the standard normal table, the p-value for the test statistic value of -0.577 is equal to 0.2820.

As the p-value is greater than 0.05, the decision is fail to reject the null hypothesis.

There is not enough evidence to support the claim that the proportion of results that is wrong is less than 10%.

Although the null hypothesis is failed to reject, the proportion of incorrect results equal to 9% is reasonably low.

Thus, it can be said that the test seems good for most purposes.