The standard error (SE) of the sampling distribution difference between two proportions is given by:
![SE=\sqrt{p(1-p)\left(\frac{1}{n_1}+\frac{1}{n_2}\right)}](https://tex.z-dn.net/?f=SE%3D%5Csqrt%7Bp%281-p%29%5Cleft%28%5Cfrac%7B1%7D%7Bn_1%7D%2B%5Cfrac%7B1%7D%7Bn_2%7D%5Cright%29%7D)
where p is the pooled sample proportion,
![n_1](https://tex.z-dn.net/?f=n_1)
<span> is the size of sample 1, and
![n_2](https://tex.z-dn.net/?f=n_%3C%2Fspan%3E2)
<span> is the size of sample 2.
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![p= \frac{p_1n_1+p_2n_2}{n_1+n_2}](https://tex.z-dn.net/?f=p%3D%20%5Cfrac%7Bp_1n_1%2Bp_2n_2%7D%7Bn_1%2Bn_2%7D%20)
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Given that a</span><span>t one vehicle inspection station, 13 of 52 trucks and 11 of 88 cars failed the emissions test.
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![p_1= \frac{13}{52} =0.25 \\ \\ p_2= \frac{11}{88} =0.125 \\ \\ n_1=52 \\ \\ n_2=88 \\ \\ p= \frac{0.25(52)+0.125(88)}{52+88} \\ \\ = \frac{13+11}{140} = \frac{24}{140} =0.1714](https://tex.z-dn.net/?f=p_1%3D%20%5Cfrac%7B13%7D%7B52%7D%20%3D0.25%20%5C%5C%20%20%5C%5C%20p_2%3D%20%5Cfrac%7B11%7D%7B88%7D%20%3D0.125%20%5C%5C%20%20%5C%5C%20n_1%3D52%20%5C%5C%20%20%5C%5C%20n_2%3D88%20%5C%5C%20%20%5C%5C%20p%3D%20%5Cfrac%7B0.25%2852%29%2B0.125%2888%29%7D%7B52%2B88%7D%20%20%5C%5C%20%20%5C%5C%20%3D%20%5Cfrac%7B13%2B11%7D%7B140%7D%20%3D%20%5Cfrac%7B24%7D%7B140%7D%20%3D0.1714)
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![SE=\sqrt{0.1714(1-0.1714)\left(\frac{1}{52}+\frac{1}{88}\right)} \\ \\ = \sqrt{0.1714(0.8286)(0.0192+0.0114)} \\ \\ = \sqrt{0.1714(0.8386)(0.0306)} = \sqrt{0.0044} \\ \\ =0.0663](https://tex.z-dn.net/?f=SE%3D%5Csqrt%7B0.1714%281-0.1714%29%5Cleft%28%5Cfrac%7B1%7D%7B52%7D%2B%5Cfrac%7B1%7D%7B88%7D%5Cright%29%7D%20%5C%5C%20%20%5C%5C%20%3D%20%5Csqrt%7B0.1714%280.8286%29%280.0192%2B0.0114%29%7D%20%20%5C%5C%20%20%5C%5C%20%3D%20%5Csqrt%7B0.1714%280.8386%29%280.0306%29%7D%20%3D%20%5Csqrt%7B0.0044%7D%20%20%5C%5C%20%20%5C%5C%20%3D0.0663)
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</span>
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Answer: Sales of jackets increased 18.8 percentage points faster than total coat sales.
Step-by-step explanation:
From the given pie-charts, Sales of jackets in 2006=213
Sales of jackets in 2007= 285
![\text{Increase in Sales of jacket = Sales in 2007-Sales in 2006}\\\\\Rightarrow\text{Increase in Sales of jacket = }285-213=72](https://tex.z-dn.net/?f=%5Ctext%7BIncrease%20in%20Sales%20of%20jacket%20%3D%20Sales%20in%202007-Sales%20in%202006%7D%5C%5C%5C%5C%5CRightarrow%5Ctext%7BIncrease%20in%20Sales%20of%20jacket%20%3D%20%7D285-213%3D72)
The percentage increase in sale of jacket =![\dfrac{\text{Increase in sales}}{\text{Sales in 2006}}\times100](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctext%7BIncrease%20in%20sales%7D%7D%7B%5Ctext%7BSales%20in%202006%7D%7D%5Ctimes100)
![=\frac{72}{213}\times100=33.8028169014\%\approx33.8\%](https://tex.z-dn.net/?f=%3D%5Cfrac%7B72%7D%7B213%7D%5Ctimes100%3D33.8028169014%5C%25%5Capprox33.8%5C%25)
Total sales in 2006=![103+297+210+213+137=960](https://tex.z-dn.net/?f=103%2B297%2B210%2B213%2B137%3D960)
Total sales in 2007=![127+223+210+285+259=1104](https://tex.z-dn.net/?f=127%2B223%2B210%2B285%2B259%3D1104)
![\text{Increase in Total coat's sales = Total sales in 2007-Total sales in 2006}\\\\\Rightarrow\text{Increase in Total sales = }1104-960=144](https://tex.z-dn.net/?f=%5Ctext%7BIncrease%20in%20Total%20coat%27s%20sales%20%3D%20Total%20sales%20in%202007-Total%20sales%20in%202006%7D%5C%5C%5C%5C%5CRightarrow%5Ctext%7BIncrease%20in%20Total%20sales%20%3D%20%7D1104-960%3D144)
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The percentage increase in total coat's sales =![\dfrac{\text{Increase in Total sales}}{\text{Total sales in 2006}}\times100](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctext%7BIncrease%20in%20Total%20sales%7D%7D%7B%5Ctext%7BTotal%20sales%20in%202006%7D%7D%5Ctimes100)
![=\frac{144}{960}\times100=15\%](https://tex.z-dn.net/?f=%3D%5Cfrac%7B144%7D%7B960%7D%5Ctimes100%3D15%5C%25)
Clearly, 33.8 >15
Hence, the percentage increase in sales of jackets is greater than percentage increase in the total coat's sales.
Difference in percent of total coats sales and jackets sales =![33.80\% -15\% =18.80\%](https://tex.z-dn.net/?f=33.80%5C%25%20-15%5C%25%20%3D18.80%5C%25)
Hence, Sales of jackets increased 18.8 percentage points faster than total coat sales.
The sentence 15 more than x is 5 written as an equation is x + 15 = 5
Answer
x + 15 = 5
A measurement used in reference of the transmitted
light as a function of wavelengths being stored in memory.