Mathematics: The federal government would like to estimate the proportion of households in the U.S. population that own their own homes. A pilot sample of 40 households found that 24 of them owned their homes. Determine the number of households that need to be sampled to construct a 99% interval with a margin of error equal to 3% to estimate the proportion.

The federal government would like to estimate the

Ответ:

dewonpruitt22

19.01.2022

Mathematics

1770

Step-by-step explanation:

We need to estimate number of households to be sampled to construct a 99% confidence interval.

Number of households to be sampled=n=?

$n=\frac{(z_{\frac{\alpha}{2} })^2 pq }{E^{2} }$

$z_{\frac{\alpha}{2} } =z_{\frac{\0.01}{2} }=z_{0.005 }=2.576$

The proportion can be estimated as

p=x/n.

We know that 24 out of 40 households owns their home.

so, x=24 and n=40.

p=24/40

p=0.6

q=1-p=1-0.6=0.4

pq=0.6*0.4=0.24

E=0.03

$n=\frac{(z_{\frac{\alpha}{2} })^2 pq }{E^{2} }$

$n=\frac{2.576^2(0.24)}{0.03^2}$

$n=\frac{1.5926}{0.0009}$

n=1769.56.

n=1770.

Thus, the number of households that need to be sampled are 1770.

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Ответ:

bubblzthechicken

10.02.2023

Mathematics

In probability, you gather data through statistics and from there, determine the chances of how likely an event is going to happen out of the total number of data you've collected. Hence, probability is always expressed as part of a whole. This can be in terms of fraction, decimal or in percentage.

You are given statistics: 12 girls and 16 boys. You solve for the total which is 12+16 = 28. This would be the denominator of your probability. For the numerator, we use the statistics for the girls. Therefore, the probability of selecting a girl to dive first is

Probability = 12/28 = 3/7 or 42.86%

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