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2 months ago

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A politician wants to estimate the proportion of constituents favoring a controversial piece of proposed legislation. suppose th

at a 99% confidence interval that extends at most 0.05 on each side of the sample proportion is required. how many sample observation are needed?

1 answer:

babunello [11.8K]2 months ago

4 0

Answer:

We have the following details:

Confidence level = 99%. Hence, the critical value at a 0.01 significance level is provided below:

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

The margin of error is mentioned in the question as:

$E=0.05$

Since we lack information about the previous proportion, we need to assume $\hat{p} = 0.5$ .

Therefore, the required sample size is:

$n=\hat{p}(1-\hat{p}) \left( \frac{z_{\frac{0.01}{2}} }{E} \right)$

$=0.5(1-0.5) \left( \frac{2.576}{0.05} \right)$

$=0.25 \times 51.52^2$

$=663.6 \approx 664$

Thus, it requires 664 sample observations.

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3400 dollars is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 25 years, to t

Leona [12618]

=3400(1+0.0825/1)^1*25
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Hope this assists!!!

6 0

1 month ago

When jumping, a flea rapidly extends its legs, reaching a takeoff speed of 1.0 m/s over a distance of 0.50 mm . part a what is t

zzz [12365]

The flea experiences an acceleration of 1,000 m/s².

Detailed explanation

This scenario involves motion with constant acceleration.

The relevant variables include the following.

$\boxed{u \ or \ v_i = initial \ velocity}$

$\boxed{u \ or \ v_t \ or \ v_i = terminal \ or \ final \ velocity}$

$\boxed{a = acceleration \ (constant)}$

$\boxed{d = distance \ travelled}$

We know the flea attains a takeoff velocity of 1.0 m/s over a distance of 0.50 mm.

The flea starts from rest, so the initial velocity is zero. The question asks for the flea's acceleration during leg extension.

The equation we apply is:

$\boxed{ \ v^2 = u^2 + 2ad \ }$

a = acceleration (m/s²)
u = initial speed = 0 m/s
v = takeoff velocity = 1.0 m/s
d = displacement = 0.50 mm

First, convert 0.50 mm to meters: $\boxed{0.50 \ mm = 0.50 \times 10^{-3} \ m = 5.0 \times 10^{-4} \ m}$

Solution steps:

Rearrange the formula to isolate acceleration (a).

$\boxed{ \ v^2 = u^2 + 2ad \ }$

$\boxed{ \ v^2 - u^2 = 2ad \ }$

$\boxed{ \ 2ad = v^2 - u^2 \ }$

$\boxed{ \ a = \frac{v^2 - u^2}{2d} \ }$

Insert the given values into the rearranged equation.

$\boxed{ \ a = \frac{(1.0)^2 - (0)^2}{2(5.0 \times 10^{-4})} \ }$

$\boxed{ \ a = \frac{1}{10 \times 10^{-4}} \ }$

$\boxed{ \ a = \frac{1}{1 \times 10^{-3}} \ }$

$\boxed{ \ a = 1 \times 10^{3}\ = 1,000 \ m/s^2 \ }$

This yields the flea's acceleration as 1,000 m/s².

Additional resources

Scientific notation: brainly.com/question/7263463
Determining substance mass: brainly.com/question/4053884
Conversion into cubic units: brainly.com/question/1446243

Keywords: flea, jumping, leg extension, takeoff velocity, initial speed, displacement, acceleration, constant acceleration, unit conversion

5 0

3 months ago

Read 2 more answers

Compare the values of the 2s and 5s in 55,220

Inessa [12570]

The number 55,220 has two 5s and two 2s. The 5s appear in the ten-thousands and thousands places, representing 50,000 and 5,000 respectively. The 2s occupy the hundreds and tens positions, corresponding to 200 and 20. In total, the 5s sum to 55,000, while the 2s add up to 220.

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3 months ago

A reporter determines a baseball player's batting average, which is a ratio of number of hits to the number of times at bats. Th

Leona [12618]

x:200

x/200 =.2121212121...

200(x/200) = 200(.2121212121...)

x = 42.4242...

The expectation is that a player would achieve 42 hits over 200 at-bats.

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2 months ago

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5.345345... can be expressed as (fraction form)

babunello [11817]

Answer:

5.(345)=1,780/333

Step-by-step explanation:

5.(345) can be calculated as (5,345 - 5)/999 which simplifies to 5,340/999, resulting in 1,780/333

8 0

2 months ago