Plz i need help figuring this out

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 $1 - \frac{\alpha}{2}$ .

Only 2 of the 11 companies were planning to increase their workforce.

This means that $n = 11, \pi = \frac{2}{11} = 0.1818$

80% confidence level

So $\alpha = 0.2$ , z is the value of Z that has a pvalue of $1 - \frac{0.2}{2} = 0.9$ , so $Z = 1.28$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1818 - 1.28\sqrt{\frac{0.1818*0.8182}{11}} = 0.033$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1818 + 1.28\sqrt{\frac{0.1818*0.8182}{11}} = 0.331$

The 80% confidence interval for the proportion of companies that are planning to increase their workforce is (0.033, 0.331).

Second question:

The margin of error is:

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

A poll taken in July 2010 estimates this proportion to be 0.36.

This means that $\pi = 0.36$

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 $Z = 1.96$ .

Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.01?

This is n for which M = 0.01. So

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

$0.01 = 1.96\sqrt{\frac{0.36*0.64}{n}}$

$0.01\sqrt{n} = 1.96\sqrt{0.36*0.64}$

$\sqrt{n} = \frac{1.96\sqrt{0.36*0.64}}{0.01}$

$(\sqrt{n})^2 = (\frac{1.96\sqrt{0.36*0.64}}{0.01})^2$

$n = 8851.04$

Rounding up(as a sample of 8851 will have a margin of error slightly over 0.01):

A sample size of 8852 is needed.

4 0

3 years ago

Amber boss tells her that she can choose whether she want to be paid 12% commission flat fee one time payment of $500. Her total

Juliette [100K]

Answer:

Amber should choose the one-time payment of $500. If amber chooses the 12% commission she would receive $474 which would be less than a payment of $500.

Step-by-step explanation:

Commission calculation:

(Total sales) * (Commission %)

(3,950) * (.12) = $474

She should choose the $500 one time payment.

5 0

2 years ago