Q 8.70 - Elementary Statistics

Question

Preliminary data analyses indicate that you can reasonably apply the z- interval procedure

Poverty and Dietary Calcium. Calcium is the most abundant mineral in the human body and has several important functions. Most body calcium is stored in the bones and teeth, where it functions to support their structure. Recommendations for calcium are provided in Dietary Reference Intakes, developed by the Institute of Medicine of the National Academy of Sciences. The recommended adequate intake (RAI) of calcium for adults (ages $19-50$) is $100$ milligrams (mg) per day. A simple random sample of $18$ adults with incomes below the poverty level gave the following daily calcium intake

Step-by-Step Solution

Answer

The sample mean is $947.39$

The $95\%$ confidence level for $\mu$ is $(860.5,1,034.2)$.

Step 1: Given Information

The daily calcium intake of eighteen adults with incomes below poverty line is given below:

Step 2: Calculation of sample mean

Mathematically,

Sample Mean, $\overline{x}=\frac{\sum x}{n}$

$=\frac{17,053}{18}$

$=947.39$

Sample mean is $947.39$.

Step 3: Calculation of Confidence Interval

For $95\%$ confidence interval,

$\overline{x}=z_{\frac{n}{2}}\left(\frac{\sigma }{\sqrt{n}}\right)=947.39\pm 1.96\left(\frac{188}{\sqrt{18}}\right)$

$=947.39\pm 86.85$

$=(860.5,1034.2)$

Therefore, $95\%$ for all adults with income below poverty line lies between $860.5$mg and $1034.5$ mg.