A sample of $n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$ is needed, in which E is the desired margin of error, as a proportion. If we find a decimal value, we round up to the next whole number.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is of:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

In a previous study of 1012 randomly chosen respondents, 374 said that there should be such a law.

This means that $n = 1012, \pi = \frac{374}{1012} = 0.3696$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

How large a sample size is needed to be 95% confident with a margin of error of E?

A sample size of n is needed, and n is found when M = E.

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$E = 1.96\sqrt{\frac{0.3696*0.6304}{n}}$

$E\sqrt{n} = 1.96\sqrt{0.3696*0.6304}$

$\sqrt{n} = \frac{1.96\sqrt{0.3696*0.6304}}{E}$

$(\sqrt{n})^2 = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$

$n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$

A sample of $n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$ is needed, in which E is the desired margin of error, as a proportion. If we find a decimal value, we round up to the next whole number.

4 0

3 years ago

Could someone help me? Thanks <3

earnstyle [38]

Answer:

Step-by-step explanation:

100 - 35 = 55 dollars remaining

55/20 = 3.25 hours until no money

4 0

2 years ago

Read 2 more answers

the cost of fencing a rectangular field at rupees 30 per metre is rupees 2400 if the length of the its field is 24m than its bre

prohojiy [21]

Answer:

breadth = 8, length = 32

Step-by-step explanation:

perimeter = 2 x (length x breadth)

= 2 x ((24 + b) + b))

= 2 x (24 + 2b)

= 48 + 4 b

48 + 4b meters costs rupees 2400

each meter costs rupees 30

so,

30 x (48 + 4b) = 2400

1440 + 120b = 2400

120b = 960

b = 8

the breadth is 8m, the length is 8 + 24 = 32m

3 0

3 years ago