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:

1786 of the 2611 were in favor, so 2611 - 1786 = 825 were opposed. Then

$n = 2611, \pi = \frac{825}{2611} = 0.316$

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:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.316 - 1.96\sqrt{\frac{0.316*0.684}{2611}} = 0.298$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.316 + 1.96\sqrt{\frac{0.316*0.684}{2611}} = 0.334$

The 95% confidence interval for those opposed is: (0.298, 0.334).

4 0

3 years ago

A classic counting problem is to determine the number of different ways that the letters of “dissipate” can be arranged. Find th

alexdok [17]

Answer:

90720 ways

Step-by-step explanation:

Since there are 9 letters, there are 9! ways to arrange them. However since there are repeating letters, we have to divide to remove the duplicates accordingly. There are 2 ‘s’ and 2 ‘i’ hence:

Number of way to arrange ‘dissipate’ = 9! / (2! x 2!) = 90720 ways

Hence there are 90720 ways to have the number of dissipate in the letter.

6 0

3 years ago

X=y<br>y=a+b×4<br>a=15-b<br>b=46-39<br>find x

katen-ka-za [31]

Answer:

the value of x is 200 I can't explain

5 0

3 years ago

Leslie and her family went out to dinner last night. The total bill was $78.44 after the 6% tax. How much was the bill before ta

sleet_krkn [62]

Answer:

$74

Step-by-step explanation:

you convert the percent to a decimal, .06, and try multiplying it with the numbers before 78, so you multiply it with 77, 76, 75, then 74, and when you multiply it with 74 you get 78.44.

Or you figure out the total amount money wise that the tax would count as and subtract that from 78.44.

5 0

3 years ago