Q 8.23RP. - Elementary Statistics

Question

Children of Diabetic Mothers. The paper "Correlations between the Intrauterine Metabolic Environment and Blood Pressure in Adolescent Offspring of Diabetic Mothers" (Journal$16$ of Pediatrics, Vol. $136$, Issue $5$, pp. $587-592$ ) by N. Cho et al. presented findings of research on children of diabetic mothers. Past studies showed that maternal diabetes results in obesity, blood pressure, and glucose tolerance complications in the offspring. Following are the arterial blood pressures, in millimeters of mercury (mm Hg). for a random sample of 16 children of diabetic mothers. 

a. Apply the $t-$interval procedure to these data to find a $95\%$ confidence interval for the mean arterial blood pressure of all children of diabetic mothers. Interpret your result in words. (Note: $\overline{x}=85.99 \mathrm{mmHg}$ and $s=8.08 \mathrm{mmHg}$.)

b. Obtain a normal probability plot, a boxplot, a histogram, and a stem-and-leaf diagram of the data.

c. Based on your graphs from part (b). is it reasonable to apply the $t-$interval procedure as you did in part (a)? Explain your answer.

Step-by-Step Solution

Answer

Part (a) We can be $95\%$ certain that the mean arterial blood pressure of all diabetes mothers' children $\mu$ is between $81.69 mm Hg$ and $90.30 mm Hg$

Part (b) 

Leaf Unit $=1.0$

Stem Leaf

$$\begin{gathered} 1 6 9 \\ 1 7 \\ 3 7 58 \\ 8 8 12244 \\ 8 8 678 \\ 5 9 014 \\ 2 9 6 \\ 1 10 1 \end{gathered}$$

Part (c) Yes.

Part (a) Step 1: Given information

81.6	84.1	87.6	82.8	82.0	88.9	86.7	96.4
84.6	101.9	90.8	94.0	69.4	78.9	75.2	91.0

Part (a) Step 2: Explanation

Now, using the $t-$interval technique, calculate the $95\%$ confidence interval for the supplied data.

$95\%$ confidence interval is, $(81.69,90.30) [u\sin g MINITAB]$

i.e., we can be $95\%$ certain that the mean arterial blood pressure of all diabetes mothers' children, $\mu$, is between $81.69 \mathrm{mmHg}$ and $90.30 \mathrm{mmHg}$

Part (b) Step 1: Explanation

Now, draw the probability plot for the given data. 

Now, construct the box plot for the given data. 

Now, construct the histogram for the given data. 

Part (b) Step 2: Calculation

Now, construct the Stem-and-leaf diagram for the given data

$Stem-and-Leaf Display: PRESSURE$

Leaf Unit $=1.0$

Stem Leaf

$$\begin{gathered} 1 6 9 \\ 1 7 \\ 3 7 58 \\ 8 8 12244 \\ 8 8 678 \\ 5 9 014 \\ 2 9 6 \\ 1 10 1 \end{gathered}$$

Part (c) Step 1: Explanation

Yes, we may use the $t-$interval technique to analyze the data. Because the sample is of a reasonable size and there are no outliers in the data, the normal probability plot suggests that the variable under discussion is generally normally distributed, as the plotted points fall roughly along a straight line.