An education fundraiser has been set up to collect donations for the most at-risk schools across the state of New York. A random sample of 500 people shows that 33% of the 250 who were contacted by telephone actually made contributions, compared with only 22% of the 250 who received email requests. Which of the formulas calculates the 99% confidence interval for the difference in the proportions of people who make donations when contacted by telephone versus those contacted by email?
Its either:
start quantity 0.33 minus 0.22 end quantity plus or minus 2.576 times the square root of start quantity 0.33 times 0.67 all over 500 plus 0.22 times 0.78 all over 500 end quantity
start quantity 0.33 minus 0.22 end quantity plus or minus 2.576 times the square root of start quantity 0.33 times 0.67 all over 250 plus 0.22 times 0.78 all over 250 end quantity

Using the z-distribution, as we are working with a proportion, the 99% confidence interval for the difference in the proportions is:

[tex](0.33 - 0.22) \pm 2.576\sqrt{\left(\sqrt{\frac{0.33(0.67)}{250}}\right)^2 + \left(\sqrt{\frac{0.22(0.78)}{250}}\right)^2}[/tex]

For each sample, we have that:

[tex]p_T = 0.33, s_T = \sqrt{\frac{0.33(0.67)}{250}}[/tex]

[tex]p_E = 0.22, s_E = \sqrt{\frac{0.22(0.78)}{250}}[/tex]

For the distribution of differences, the mean is the subtraction of the means, hence:

[tex]p = p_T - p_E = 0.33 - 0.22[/tex]

The standard error is the square root of the sum of the variances, hence:

[tex]s = \sqrt{s_T^2 + s_E^2} = \sqrt{\left(\sqrt{\frac{0.33(0.67)}{250}}\right)^2 + \left(\sqrt{\frac{0.22(0.78)}{250}}\right)^2}[/tex]

It is given by:

[tex]p \pm zs[/tex]

99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.576.

Then, the interval is:

[tex](0.33 - 0.22) \pm 2.576\sqrt{\left(\sqrt{\frac{0.33(0.67)}{250}}\right)^2 + \left(\sqrt{\frac{0.22(0.78)}{250}}\right)^2}[/tex]

To learn more about the z-distribution, you can check https://brainly.com/question/25890103

What is the central idea of the article Elephants Attack as Humans Turn Up the Pressure?

a) Scientists are developing new ways to prevent elephants from attacking humans and ruining their crops.

b) The number of elephant attacks against humans has been rising in both Asia and Africa.

c) Researchers think that stresses created by humans are the reason behind increasing numbers of elephant attacks.

d) Elephants react differently to pressures from humans than they do to competition from other elephants.

What part of the dairy industry makes the most profit?

A1 does kilogram block slides down a frictionless inclined plane 2.5 M High what is the velocity of the bottom of the plane assume gravitational acceleration is 9.8 Ms is it 2.5 mm is 3.9 m s 7.0 m s r 9.8 m s?

Which statement best characterizes power relations among the centers of Eurasian civilizations as they approached the year 1450?

a. Islamic caliphates are reaching the height of their power and influence
b. Ming rulers of China have redoubled their efforts to move to the center of maritime trading networks in the East Asian and Indian Ocean
c. A power vacuum of sorts has opened, as Byzantine, Abbasid, and Ming Chinese powers become less of a force in global affairs
d. Western Europe dominates world trade
e. South and East Asia are no longer important sources of luxury items in long-distance trade networks and become increasingly isolated

Why can judicial review in combination with the nature of Supreme Court tenure lead to controversy, primarily about the Court’s legitimacy?

a. The legislature can override Supreme Court decisions, but the executive branch cannot.

b. Other branches of government can only address Supreme Court decisions in limited ways.

c. Supreme Court justices serve at the will of the president and thus are beholden to him or her.

d. The nature and powers of the Supreme Court were never fully established by the Constitution.

A researcher wants to determine whether there is a relationship between age and frequency of travel. In a random sample of 18- to 25-year-olds, 70 of 195 traveled more than twice each year. In a random sample of 55- to 62-year-olds, 205 of 230 traveled more than twice each year. What is the margin of error for a 98% confidence interval for the difference between the proportions of travelers in these age groups who travel more than twice each year?

1.3180
0.5656
0.0931
0.0400
0.0016

When evaluating an argument, one should always take into consideration the existence and merit of any unstated premises. t or f

3. Which renewable resource is a vital source of energy for all living things? wind solar biomass hydropower

You're in a car listening to Ransom for 10 minutes. You send 20 texts in that time. You then listen to Panini for 30 minutes and send 30 texts in that time. How fast is the car moving?

(Show all work)

I don't care I chose
Advanced Placement (AP

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