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It is given in the question that,

The proportion of high school graduates that will pass the basic literacy test=$80$%

The proportion of high school dropouts that will pass basic literacy test =$40$%

Number of Random Sample from high school graduates for basic literacy test =$60$

Number of Random Sample from high school dropouts for basic literacy test =$75$

Let $p1$be the percentage of high school graduates who pass a basic literacy exam, and $p2$be the proportion of high school dropouts who pass a basic literacy test. $p1-p2$'s sampling distribution is Normal because:

localid="1650446649236" $$\begin{gathered} n_1{p}_1=60脳0.80 \\ =48 \end{gathered}$$

localid="1650446659437" $$\begin{gathered} n_1(1鈭�p_1)=60脳0.20 \\ =12 \end{gathered}$$

localid="1650446668572" $$\begin{gathered} n_2{p}_2=75脳0.40 \\ =30 \end{gathered}$$

localid="1650446679632" $$\begin{gathered} n_2(1鈭�p_2)=75脳0.60 \\ =45 \end{gathered}$$

$\text{Are at least}10\text{, the sampling distribution of}{\hat{p}}_1鈭�{\hat{p}}_2\text{is approximately Normal. Its mean is:}$

${渭}_{\stackrel{藱}{A}鈭�{\stackrel{藱}{p}}_2}=p_1鈭�p_2$

$=0.80-0.40$

$=0.40$

The standard deviation is:

${蟽}_{i鈭�{\stackrel{藱}{p}}_2}=\sqrt{\frac{p_1(1鈭�p_1)}{n_1}+\frac{p_2(1鈭�p_2)}{n_2}}$

$=\sqrt{\frac{0.8脳(1鈭�0.8)}{60}+\frac{0.40脳(1鈭�0.40)}{75}}$

$=0.0766$

Hence,

$p({\hat{p}}_1鈭�{\hat{p}}_2鈮�0.2)=p(z鈮�\frac{0.2鈭�0.40}{0.0766})$

$=P(z鈮�鈭�2.61)$ (from the normal table)

$=1鈭�P(z鈮�鈭�2.61)$

$=1-0.00453$

$=0.9955$

It is given in the question that,

The proportion of high school graduates that will pass the basic literacy test=$80$%

The proportion of high school dropouts that will pass basic literacy test =$40\%$

Number of Random Sample from high school graduates for basic literacy test =$60$

Number of Random Sample from high school dropouts for basic literacy test =$75$

Yes, the claim of the researcher should be questioned. The probability that at least $0.20$or $20$% more graduates pass the test than dropouts pass is $0.9955$. There is a $99.55$% likelihood of receiving samples with at least $20$% more high school graduates passing, but only a $0.45$percent risk of receiving samples with no more than $20$% more high school graduates passing.