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The Null Hypothesis is,

$H_0:\mathrm{μ}=18mg$.

The Alternative Hypothesis is,

$H_0:\mathrm{μ}<18mg$.

According to the definition of the type I error it is to reject a null hypothesis when it is true. A type I error would occur in fact $H_0:\mathrm{μ}=18mg$true, that is the RDA of iron for adult females of age $51$is $18$mg but the result of the sampling lead to conclude that the mean RDA of females of age $51$is less than $18$mg.

According to the definition of the type II error, it is to not reject a null hypothesis when it $\left(H_0\right)$is false. A type II error would occur in fact localid="1651257139706" $\mathrm{μ}=18mg$is not to be rejected, but the results of the sampling fall to lead to conclude that the mean RDA of females of age$51$is less than$18$mg.$18$

A correct decision would occur if the true null hypothesis is not rejected or a false null hypothesis is rejected. Here, in the fact the mean RDA of adult females is $\mathrm{μ}=18mg$and the results of the sampling do not lead to rejection, so is a correct decision; or the mean RDA of adult males is$\mathrm{μ}<18mg$ and the results of the sampling lead to that conclusion.

Here, the mean iron intake of adult females of $51$years old is $18mg$per day, and the results of a hypothesis test lead to rejection of the null hypothesis.

We are rejecting the true null hypothesis of $\mathrm{μ}=18mg$, where it is also obtained as a sampling result. So, we are committing a Type I error.

Here, the mean iron intake of adult females of $51$years old is less than$18mg$per day, and the results of a hypothesis test lead to rejection of the null hypothesis.

As a sampling result, we obtain the mean RDA of adult females of $51$years old is less than $18mg$per day, and we are rejecting the null hypothesis that the mean of adult females of $51$years old is less than $18mg$per day. Therefore, our decision is a correct decision.