Q.73 - The Practice of Statistics for AP

Question

The recommended daily allowance (RDA) of calcium for women between the ages of 18 and 24 years is 1200 milligrams (mg). Researchers who were involved in a large-scale study of women’s bone health suspected that

their participants had significantly lower calcium intakes than the RDA. To test this suspicion, the researchers measured the daily calcium intake of a random sample of 36 women from the study who fell in the desired age range. The Minitab output below displays descriptive statistics for these data, along with the results of a significance test.

(a) Determine whether there are any outliers. Show your work.

(b) Interpret the P-value in context.

(c) Do these data give convincing evidence to support the researchers’ suspicion? Carry out a test to help your answer

Step-by-Step Solution

Answer

a. There are no outliers

b.$0.00$

c. There is convincing evidence to support the researchers’ suspicion 

Step 1: Given Information

The recommended daily allowance (RDA) of calcium for women between the ages of $18$ and $24$ years is $1200$ milligrams (mg). The researchers measured the daily calcium intake of a random sample of $36$ women from the study who fell in the desired age range.  

Step 1: Explanation Part (a)

we know from the tab,

$Q_1=632.5\text{ and }{Q}_3=1090.5$

$1QR=Q_3-Q_1=1090.5-632.5=458$

Calculating the lower and upper boundaries,

$\begin{array}{r}\mathrm{LB}=Q_1-1.5\times 1QR=632.5-1.5\times 458=-54.5\\ \text{UB}=Q_3+1.5\times 1QR=1090.5+1.5\times 458=1777.5\end{array}$

Hence we can say that all the values lie between the boundaries and there is no outlier.

Step 2: Explanation Part (b)

The probability of getting a random sample of $36$ ladies with a typical intake $856.2$ is close to zero if the typical daily calcium intake of ladies is $1200$ mg. It additionally infers that the typical intake among $36$ example of ladies is under $1200$.

Step 3: Explanation Part (c)

Calculating the null and alternative hypotheses,

$\begin{array}{r}{H}_0:\mu =1200\\ H_a:\mu <1200\end{array}$

A random selection of $36$ women is done. The population is of huge size, so we can approximately expect it to be an ordinary distribution. There will be in excess of $360$ ladies in U.S matured somewhere in the range of $18$ and $24$, so $10\%$ condition is additionally satisfied.

t test is done and we get test statistic t= $-6.73$and the corresponding p value as $0.000$. As the p-value is not exactly the degree of significance $0.005$, we have sufficient evidence at $5\%$ level of significance to dismiss the null hypothesis. Hence, there is convincing evidence to support the researchers’ suspicion