91Ó°ÊÓ

The given values are,

$$\begin{gathered} x_1=386, \\ {n}_1=750, \\ {x}_2=237, \\ {n}_2=500, \\ \mathrm{Î\pm }=0.05 \end{gathered}$$

The formula for ${\tilde{p}}_1$is given by,

${\tilde{p}}_1=\frac{x_1}{n_1}$

The formula for ${\tilde{p}}_2$is given by,

${\tilde{p}}_2=\frac{x_2}{n_2}$

The formula for$z$is given by,

$z=\frac{{\tilde{p}}_1-{\tilde{p}}_2}{\sqrt{{\tilde{p}}_p\left(1-{\tilde{p}}_p\right)}\sqrt{\frac{1}{n_1}+\frac{\mathrm{Γ}}{m_2}}}$

The formula for${\tilde{p}}_p$is given by,

${\tilde{p}}_p=\frac{x_1+x_2}{n_1+n_2}$

The value of$n_1-x_1$is calculated as,

$$\begin{gathered} n_1-x_1=2701-35 \\ =2666 \end{gathered}$$

The value of$n_2-x_2$is calculated as,

$$\begin{gathered} n_2-x_2=2052-47 \\ =2005 \end{gathered}$$

The values $x_1,\left(n_1-x_1\right),x_2$, and $\left(n_2-x_2\right)$are all greater than 5 .

The value of${\tilde{p}}_1$is calculated as,

$$\begin{gathered} {\tilde{p}}_1=\frac{x_1}{n_1} \\ =\frac{386}{750} \\ =0.514\backslash \end{gathered}$$

The value of ${\tilde{p}}_2$is calculated as,

$$\begin{gathered} {\tilde{p}}_2=\frac{x_2}{n_2} \\ =\frac{237}{500} \\ =0.474 \end{gathered}$$

The value of ${\tilde{p}}_p$is calculated as,

$$\begin{gathered} {\tilde{p}}_p=\frac{x_1+x_2}{n_1+n_2} \\ =\frac{386+237}{750+500} \\ =0.4984 \end{gathered}$$

Assumptions:

The selected sample should be a simple random sample from two populations.

The samples are independent of one another.$x_1,n_1-x_1,x_2$and $n_2-x_2$are all at least 5.

The two samples are random samples, the sample is independent of each other and the$x_1,n_1-x_1,x_2$ and$n_2-x_2$ are all at least 5 .

Therefore, the assumptions for two proportions are satisfied.

The given values are,

$$\begin{gathered} x_1=386, \\ {n}_1=750, \\ {x}_2=237, \\ {n}_2=500, \\ \mathrm{Î\pm }=0.05 \end{gathered}$$

The null hypothesis:

$H_0:p_1>p_2$

The alternative hypothesis:

$H_a:p_1>p_2$

Using the MINITAB output.

MINITAB output: Test and Cl for two proportions.

From MINITAB output, the test statistic is $1.41$and $p-$value is $0.079$

$p$- value is greater than the level of significance.

$p\text{- value}(=0.079)>\mathrm{Î\pm }(=0.05)\text{.}$

The null hypothesis is rejected.

There is no evidence to suggest that those with a bachelor's degree have a higher percentage of adults who are overweight than those with a graduate degree.

As a result, there is no evidence to suggest that those with a bachelor's degree have a higher percentage of adults who are overweight than those with a graduate degree.