Mathematics: Can someone me what is proportions in maths. and give an example question!

We have to flip the coin 78 times.Step-by-step explanation:In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.In whichz is the zscore that has a pvalue of .The margin of error is:We suspect that the coin is fair. This means that 96.5% confidence levelSo , z is the value of Z that has a pvalue of , so . How many times would we have to flip the coin in order to obtain a 96.5% confidence...

Can someone me what is proportions in maths. and

Ответ:

joeydjky

17.01.2023

Mathematics

We have to flip the coin 78 times.

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:

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

We suspect that the coin is fair.

This means that $\pi = 0.5$

96.5% confidence level

So $\alpha = 0.035$ , z is the value of Z that has a pvalue of $1 - \frac{0.035}{2} = 0.9825$ , so Z = 2.108 .

How many times would we have to flip the coin in order to obtain a 96.5% confidence interval of width of at most .12 for the probability of flipping a head?

n times, and n is found when M = 0.12. So

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

$0.12 = 2.108\sqrt{\frac{0.5*0.5}{n}}$