The paper "Correlations Between the Intrauterine Metabolic Environment and Blood Pressure in adolescent Offspring of Diabetic Mothers" (Journal 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 have shown that maternal diabetes results in obesity, blood pressure, and glucosetolerance complications in the offspring. The WeissStats site provides data on systolic blood pressure, in mmHg from independent random samples of 99 adolescent offspring of diabetic mothers (ODM) and 80 adolescent offspring of nondiabetic mothers (ONM).

a. Obtain normal probability plots, boxplots, and the standard deviations for the two samples.

b. At the$5\%$ significance level, do the data provide sufficient evidence to conclude that the mean systolic blood pressure of ODM children exceeds that of ONM children?

c. Determine a $95\%$confidence interval for the difference between the mean systolic blood pressures of ODM and ONM children.

d. Are your procedures in parts (b) and (c) justified? Explain your answer.

The paper "Correlations Between the Intrauterine Metabolic Environment and Blood Pressure in adolescent Offspring of Diabetic Mothers" (Journal 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 have shown that maternal diabetes results in obesity, blood pressure, and glucosetolerance complications in the offspring. The WeissStats site provides data on systolic blood pressure, in $\mathrm{mm} \mathrm{Hg}$, from independent random samples of 99 adolescent offspring of diabetic mothers (ODM) and 80 adolescent offspring of nondiabetic mothers (ONM).

We need to obtain normal probability plots, boxplots, and the standard deviations for the two samples.

The number of samples is provided as $\left(n\right)$.

$99$from a diabatic mother

$80$from a nondiabatic mother

Create 51 and 53 vegetarian and omnivore female samples in MATLAB using the "norminv" function with the provided mean and standard deviation.

$x_1=randi\left(\right[85,149],99,1)$

$x_2=randi\left(\right[83,142],80,1)$

After that, we'll produce the normal probability and boxplot using random samples.

clc

clear

close all

r 1=r a n d i([85,149], 99,1);

r 2=r a n d i([83,142], 80,1);

figure (1)

f= normplot (r 1);

f(1). Linewidth=1.2;

f(2). Linewidth=1.2;

set (gca, 'linewidth', 1.2, 'fontsize', 12);

box on

clc

clear

close all

r 1= randi ([85,149], 99,1) ;

r 2= randi ([83,142], 80,1) ;

figure (1)

f=normplot(r1);

f(1) . Linewidth=1.2;

f(2).Linewidth=1.2;

set(gca,'linewidth', 1.2,'fontsize', 12);

box on

axis square

figure (2)

s=normplot(r2);

s(1). Linewidth=1.2;

s(2). Linewidth=1.2;

set(gca,'linewidth', 1.2, 'fontsize', 12);

box on

axis square

figure (2)

s= normplot (r 2);

s(1). Linewidth=1.2;

s(2). Linewidth=1.2;

set (gca, 'linewidth', 1.2, 'fontsize', 12);

box on

axis square

figure (3)

boxplot(r1)

axis square

figure (4)

boxplot (r 2)

axis square

Query:

- First, we've established the sample size.

- Then, using the "randi" function, generate random samples with the supplied mean and standard deviation.

- Make a boxplot and a normal probability plot with your data.

Given in the question that,the paper "Correlations Between the Intrauterine Metabolic Environment and Blood Pressure in adolescent Offspring of Diabetic Mothers" (Journal 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 have shown that maternal diabetes results in obesity, blood pressure, and glucosetolerance complications in the offspring. The WeissStats site provides data on systolic blood pressure, in $\mathrm{mmHg}$, from independent random samples of 99 adolescent offspring of diabetic mothers (ODM) and 80 adolescent offspring of nondiabetic mothers (ONM).

We need to check that whether the data provide sufficient evidence to conclude that the mean systolic blood pressure of ODM children exceeds that of ONM children at the $5\%$significance level,

The number of samples is provided as $n$.

$99$from a diabatic mother

$80$from a nondiabatic mother

Using the relation, calculate the mean for vegetarian females.

${\overline{x}}_1=\frac{{\sum }_{i=1}^n{x}_i}{n}$

Substitute the values and solve

${\overline{x}}_1=\frac{{\sum }_{i=1}^n{x}_i}{n}=\frac{127+137+\dots +114+128}{99}$

then we will get

${\overline{x}}_1=\frac{{\sum }_{i=1}^n{x}_i}{n}=\frac{127+137+\dots +114+128}{99}=118$

For omnivores females

${\overline{x}}_2=\frac{{\sum }_{i=1}^n{x}_i}{n}=\frac{99+111+\dots +89+103}{80}=109.9875$

Using relation, calculate the standard deviation for both females.

$s_1=\sqrt{\frac{{\sum }_{i=1}^n{\left(x_i-{\overline{x}}_1\right)}^2}{n-1}}=12.0374$

$s_1=\sqrt{\frac{{\sum }_{i=1}^n{\left(x_i-{\overline{x}}_1\right)}^2}{n-1}}=11.2481$

Given in the question that,the paper "Correlations Between the Intrauterine Metabolic Environment and Blood Pressure in adolescent Offspring of Diabetic Mothers" (Journal 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 have shown that maternal diabetes results in obesity, blood pressure, and glucosetolerance complications in the offspring. The WeissStats site provides data on systolic blood pressure, in $\mathrm{mmHg}$, from independent random samples of 99 adolescent offspring of diabetic mothers (ODM) and 80 adolescent offspring of nondiabetic mothers (ONM).

We need to determine a $95\%$confidence interval for the difference between the mean systolic blood pressures of ODM and ONM children.

The number of sample $\left(n\right)$

mean $\left(\overline{x}\right)$

standard deviation $\left(\sigma \right)$

The degree of freedom will be used to construct the $99$percent confidence interval.

$df=n_1+n_2-2=99+80-2=177$

The $t$distribution of students will be

$t_{\alpha /2}=1.984$

Using the connection, calculate the pool standard deviation.

$s_p=\sqrt{\frac{\left(n_1-1\right)s_1{}^2+\left(n_2-1\right){s_2}^2}{n_1+n_2-2}}$

Place all of the values for resolving the relationship.

$s_p=\sqrt{\frac{(99-1)(12.0374{)}^2+(80-1\left)\right(11.2481{)}^2}{99+80-2}}$

$s_p=11.6917$

Using the relation, calculate the marginal error.

$E=t_{\alpha /2}·s\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$

we will get

$E=1.984\times 11.6917\sqrt{\frac{1}{99}+\frac{1}{80}}$

$E\approx 3.4873\$$

Determine the $95\%$confidence interval.

$\left({\overline{x}}_1-{\overline{x}}_2\right)-E=(118-109.9875)-3.4873=4.5252$

$\left({\overline{x}}_1-{\overline{x}}_2\right)+E=(118-109.9875)+3.4873=11.4998$

The $95\%$confidence interval will be

$95\%\text{Cofidence interval}=\left[\begin{array}{ll}4.5252& 11.4998\end{array}\right]$

The paper "Correlations Between the Intrauterine Metabolic Environment and Blood Pressure in adolescent Offspring of Diabetic Mothers" (Journal 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 have shown that maternal diabetes results in obesity, blood pressure, and glucosetolerance complications in the offspring. The WeissStats site provides data on systolic blood pressure, in$mmHg$, from independent random samples of 99 adolescent offspring of diabetic mothers (ODM) and 80 adolescent offspring of nondiabetic mothers (ONM).

We need to verify that whether our procedures in parts (b) and (c) are justified

The data originate from a population with a normal distribution if the normal probability plot is linear.