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sleet_krkn [62]
3 years ago
12

6) On Cupcake Wars, the bakers must fill 1000 cupcake cones in the final challenge!

Mathematics
1 answer:
kupik [55]3 years ago
6 0

Answer:

Don't know the answer to bad for u hahahahahah

Step-by-step explanation: get better

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Mo spends £15 on ingredients to make 40 cookies.
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Given :

Mo spends £15 on ingredients to make 40 cookies.

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The Mo's percentage profit.

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T = £2000/66.09  

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In 2010, the Census Bureau estimated the proportion of all Americans who own their homes to be 0.669. An urban economist wants t
Alexxandr [17]

Answer:

i)

Sample size making use of the Census Bureau: 1,499 American adults.

Sample size without making use of the Census Bureau: 1,692 American adults

ii)

71

Step-by-step explanation:

i)

The sample size n in Simple Random Sampling is given by

\bf n=\frac{z^2p(1-p)}{e^2}

where  

<em>z = 1.645 is the critical value for a 90% confidence level </em><em>(*) </em>

<em>p= 0.669 is the population proportion given by the Census  </em>

<em>e = 0.02 is the margin of error </em>

so  

\bf n=\frac{(1.645)^2*0.669*0.331}{0.02^2}=1,498.05\approx 1,499

rounded up to the nearest integer.

(*)This is a point z such that the area under the Normal curve N(0,1) 1nside the interval [-z, z] equals 90% = 0.9

<em>It can be obtained with tables or in Excel or OpenOffice Calc with </em>

<em>NORMSINV(0.95) </em>

<em> </em>

If she ignores the Census estimate, the she has to take the largest sample possible that meets the requirements.

Let's show it is obtained when p = 0.5

As we said, the sample size n is

\bf n=\frac{z^2p(1-p)}{e^2}

where  

e = 0.02 is the error proportion  

z = 1.645

hence

\bf n=\frac{(1.645)^2p(1-p)}{(0.02)^2}=6765.0625p(1-p)=6765.0625p-6765.0625p^2

taking the <em>derivative</em> with respect to p, we get

n'(p)=6765.0625-2*6765.0625p

and  

n'(p) = 0 when p=0.5

By taking the second derivative we see n''(p)<0, so p=0.5 is a maximum of n

<em>This means that if we set p=0.5, we get the maximum sample size for the confidence level required for the proportion error 0.02 </em>

Replacing p with 0.5 in the formula for the sample size we get

\bf n=6765.0625*0.5-6765.0625(0.5)^2=1691.27\approx 1,692

rounded to the nearest integer.

ii)

When we do not have a proportion but a variable whose approximate standard deviation s is known, then the sample size n in Simple Random Sampling is given by

\bf n=\frac{z^2s^2}{e^2}

where  

<em>z = 2.241 is the critical value for a 95% confidence level </em><em>(*) </em>

<em>s = 7.5 is the estimated population standard deviation </em>

<em>e = 2 hours is the margin of error </em>

so  

\bf n=\frac{z^2s^2}{e^2}=\frac{(2.241)^2(7.5)^2}{(2)^2}=70.62\approx 71

(*)This is a point z such that the area under the Normal curve N(0,1) inside the interval [-z, z] equals 95% = 0.95

<em>It</em> <em>can be obtained in Excel or OpenOffice Calc with </em>

<em>NORMSINV(0.9875) </em>

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