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:

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

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 $Z = 1.96$ .

What sample size could be 95% confident that the estimated (sample) proportion is within 4 percentage points of the true population proportion?

Sample size of at least n when $M = 0.04$

42.1% of women-owned businesses provided retirement plans contributions, which means that $p = 0.421$ . So

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

$0.04 = 1.96\sqrt{\frac{0.421*0.579}{n}}$

$0.04\sqrt{n} = 0.9677$

$\sqrt{n} = \frac{0.9677}{0.04}$

$\sqrt{n} = 24.19$

$\sqrt{n}^{2} = (24.19)^(2)$

$n = 585.2$

We need a sample size of 586 or higher.

3 0

3 years ago

What is the complex conjugate of 7 + 8i ?

Lady bird [3.3K]

Answer:

7-8i

Step-by-step explanation:

to find as complex conjugate, simply change the sign of the imaginary pert (the part with the i). this means that is either goes from positive to negetive or from negetive to positive

as as general rule,the complex conjugate of a +bi is a-bi

3 0

3 years ago

Ginger spent $24 at the fair, which was three times the amount she spent last year at the fair. How much money did Ginger spend

zubka84 [21]

Answer:

She spent 8 dollars.

Step-by-step explanation:

24 divided by 3 is 8

5 0

3 years ago

If the sales tax in Alabama is 4 percent and a $20.00 purchase is made. What is the sales price? What is the total purchase pric

mihalych1998 [28]

Hello there! So first off, let's find the tax. In order to find the tax of an item, all you have to do is multiply the price by the percentage, because the tax is the portion of the price. The tax is 4%. Let's solve. 20 * 4% (0.04) is 0.8. The tax is $0.80. Let's add that to the purchase price. 20 + 0.80 is 20.80. That's the total purchase price. Here are the answers easier to read.

Sales tax: $0.80
Total price: $20.80

8 0

3 years ago