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

For this problem, we have that:

$n = 1000, p = \frac{260}{1000} = 0.26$

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 $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.26 - 1.96\sqrt{\frac{0.26*0.74}{1000}} = 0.2328$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.26 + 1.96\sqrt{\frac{0.26*0.74}{1000}} = 0.2872$

The 95% confidence interval for the proportion of corporations preferring a nonsmoking candidate is (0.2328, 0.2872)

4 0

2 years ago

What is the surface area of a cube if each side length is 5 inches?

levacccp [35]

Answer:║

∨

A=150in²

Hope this helps :D

3 0

3 years ago

Read 2 more answers

Determine if each of the numbers below is a solution to the inequality 3x-2<2-2x. SHOW ALL OF YOUR WORK

rodikova [14]

Answer:

b, c, and d are solutions

Step-by-step explanation:

3x - 2 < 2 - 2x

5x - 2 < 2

5x < 4

x < 4/5

b) 1/2 < 4/5 true

c) -3 < 4/5 true

d) 2/3 < 4/5 true

7 0

3 years ago

The set of multiples of 8 which are greater than 20 but less than 40​

The set of multiples of 8 which are greater than 20 but less than 40