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The null hypothesis, denoted by H₀, is the claim that is initially assumed to be true (the 鈥減rior belief鈥� claim). The alternative hypothesis, denoted by H_a, is the assertion that is contradictory to H₀.

The null hypothesis will be rejected in favour of the alternative hypothesis only if sample evidence suggests that H₀ is false. If the sample does not strongly contradict H₀, we will continue to believe in the plausibility of the null hypothesis. The two possible conclusions from a hypothesis-testing analysis are then reject H0 or fail to reject H₀.

The hypothesis of interest are \({H_0}:\mu = 15\) versus \({H_a}:\mu < 15\)

Assumption that the sample is from normal population distribution with known standard deviation allows using test statistic:

\(z = \frac{{\overline X - {\mu _0}}}{{\sigma /\sqrt n }}\)

The \(n\) is big enough to assume this. This z statistic value is

\(\begin{array}{l}z = \frac{{11.3 - 15}}{{6.43/\sqrt {115} }}\\z = - 6.17\end{array}\)

The critical value \({z_\alpha }\), for \(\alpha = 0.05\)(other level of significance could have been chosen), because of one sided testing is,

\(\begin{array}{l}{z_\alpha } = {z_{0.05}}\\{z_\alpha } = 1.645\end{array}\)

The fact ,

\(\begin{array}{l}z = - 6.17 < - 1.645\\z = - {z_\alpha }\end{array}\)

Implies that the null hypothesis is rejected at \(0.05\) level of significance. This is because the area to the left of \( - 6.17\) under the standard normal curve is smaller than the area to the left of \( - 1.645\) under the standard normal curve ( this implies that the P value is smaller than \(0.05\)).

The conclusion is that the average daily intake falls below the recommended daily allowance \(15mg/day\).