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Step1/6Given: Total number of students \((n) = 200\).Total number of girls \((n_1) = 80\).Total number of girls surveyed \((x_1) = 60\).Total number of boys \((n_2) =120\).Total number of boys surveyed \((x_2)=80\).Confidence level: 0.95.Step2/6Difference between proportions of girls and proportion of boys \((\hat p_1-\hat p_2)\).Proportion of girls \((\hat p_1)\);\(\hat p_1=\frac{x_1}{n_1}\)\(\hat p_1=\frac {60}{80}\)\(=0.75\)The Proportion of boys \((\hat p_2)\)\(\hat p_2=\frac{x_2}{n_2}\)\(=0.666\)Then a formula for the difference between the proportions of girls and proportion of boys is\((\hat p_1-\hat p_2)=0.75-0.67\)\(=0.08\)Explanation: The formula for sample proportion is   .Step3/6The standard error of the difference between the proportions of girls and the difference between the two proportions.Then by formula for standard error,\(\text{standard error}=\sqrt{\frac { 0.75 \times (1-0.75)}{80}+ \frac{0.67 \times (1-0.67)}{120}}\)\(\text{standard error}=\sqrt{\frac { 0.75 \times 0.25}{80}+ \frac{0.67 \times 0.33}{120}}\)\(\text{standard error}=0.0647\)Explanation:  Step4/6The 95% confidence interval for the difference between the two proportions is obtained below:\(\text{confidence interval}=( ( \hat p_1 -\hat p_2) - Z_\frac{\alpha}{2} \times \text{Standard error} , (\hat p_1 -\hat p_2) + Z_\frac{\alpha}{2} \times\text{ Standard error})\)\(=({0.08}-1.96\times 0.0667 ,{0.08}+1.96 \times 0.0667)\)\(=(0.08-0.1268 , 0.08+0.1268)\)\(\text{confidence interval}=( -0.0468 , 0.2068)\)Explanation:Where,    is critical value,Critical value is obtained by Excel function.The Excel function is “=NORM.S.INV(0.05/2)”.Step5/6Yes,it is the correct interpretation.Explanation:The 90% confidence interval for the difference between two proportion is (-0.0233,0.1900). Then the correct interpretation is we are 90% confident that the true difference between the proportion that girls and boys who prefer Math to English is lies between (-0.0233,0.1900).Step6/6Yes, based on this data we conclude that among elementary students girls like math more than boys.Explanation:The proportion of girls is 0.75 which is greater than the proportion of boys is 0.67.Final Answer:a)The difference between the proportion of girls and the proportion of boys is 0.08.b)The standard error of the difference between the proportions of girls and the difference between the two proportions is 0.0647.c)The 95% confidence interval for the difference between the two proportions is ( -0.0468, 0.2068).d)Yes, it is the correct interpretation.e)Yes, based on this data we conclude that among elementary students girls like math more than boys. ...