Mathematics: The 2004 presidential election exit polls from the critical state of ohio provided the following results. there were 2020 respondents in the exit polls and 768 were college graduates. of the college graduates, 412 voted for george bush. (a) calculate a 99% confidence interval for the proportion of college graduates in ohio that voted for george bush. round the answers to 3 decimal places. (b) calculate a 95% lower confidence bound for the proportion of college graduates in ohio that voted for george

The 2004 presidential election exit polls from

ellie55991

07.01.2022

a) $0.490\leq p\leq0.582$

b) $0.501\leq p$

Step-by-step explanation:

Given : Sample size of respondents in the exit polls : n= 2020

Number of respondents voted for George Bush = 412

Sample proportion: $\hat{p}=\dfrac{412}{768}\approx0.536$

a) Critical value for 99% confidence level : $z_{\alpha/2}=2.576$

Confidence interval for proportion:-

$\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$=0.536\pm (2.576)\sqrt{\dfrac{0.536(1-0.536)}{768}}\\\\=0.536\pm0.046\\\\=(0.490,\ 0.582)$

Hence, the 99% confidence interval for the proportion of college graduates in Ohio that voted for George Bush: $0.490\leq p\leq0.582$

b) Critical value for 95% confidence level : $z_{\alpha/2}=1.96$

Lower confidence bound for the proportion :

$\hat{p}- z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.536-(1.96)\sqrt{\dfrac{0.536(1-0.536)}{768}}\\\\=0.536-0.035=0.501$

Hence, a 95% lower confidence bound for the proportion of college graduates in Ohio that voted for George Bush : $0.501\leq p$

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mandy9386

18.06.2020

37.625 square yards or 37⅝ square yards

Step-by-step explanation:

Area of the triangle = ½*base*height

Where,

base = 10¾ yd = 10.75 yds

height = 7 yds

Substitute the value of each variable into the equation:

Area = ½*10.75*7

Area = 37.625 square yards or 37⅝ square yards

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