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2 years ago

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The culinary herb cilantro, Coriandrum sativum, is very polarizing; some people love it and others hate it. A genetic component

is suspected to be at play. A survey of 12087 American adults of European ancestry asked whether they like or dislike the taste of cilantro. A total of 3181 said that they dislike the taste of cilantro.
(a) Estimate with 95% confidence (and interpret) the proportion of all American adults of European an- cestry who dislike the taste of cilantro
(b) Estimate with 95% confidence (and interpret) a lower confidence bound for the proportion of all Amer- ican adults of European ancestry who dislike the taste of cilantro

1 answer:

nataly862011 [7]2 years ago

3 0

Answer:

The 95% confidence (and interpret) the proportion of all American adults of European an- cestry who dislike the taste of cilantro

( 0.2552 , 0.2709)

b) The lower bound for the proportion of all American adults of European ancestry who dislike the taste of cilantro is 0.2552

Step-by-step explanation:

<u>Explanation:</u>-

Given data a survey of 12087 American adults of European ancestry asked whether they like or dislike the taste of cilantro.

large sample size 'n' = 12087 American adults

in survey A total of 3181 said that they dislike the taste of cilantro.

so The sample proportion 'p' = $\frac{3181}{12087} = 0.2631$

a) Estimate with 95% confidence (and interpret) the proportion of all American adults of European ancestry who dislike the taste of cilantro.

$(p - 1.96 \sqrt{\frac{pq}{n} } ,p + 1.96\sqrt{\frac{pq}{n} } )$

$(0.2631 - 1.96 \sqrt{\frac{0.2631 X 0.7369}{12087} } ,0.2631 + 1.96\sqrt{\frac{0.2631 X 0.7369 }{12087} } )$

(0.2631 - 0.00784 , 0.2631 + 0.00784 )

( 0.2552 , 0.2709)

b) The lower bound for the proportion of all American adults of European ancestry who dislike the taste of cilantro is 0.2552

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