In a recent survey of 200 elementary students, many revealed they preferred math than English. Suppose that 80 of the students surveyed were girls and that 120 of them were boys. In the survey, 60 of the girls, and 80 of the boys said that they preferred math more. Required:
a. Calculate an 80% confidence interval for the difference in proportions.
b. What is the standard error of the difference in the probability between that girls prefer math more and boys prefer math more?

1. 0.4097
2. 0.0042
3. 0.0833
4. 0.0647734

c. What is the difference in the probability between that girls prefer math more and boys prefer math more?

1. 0.0833
2. 0.5
3. 0.0042
4. 0.4097

Step-by-step explanation:

a) Confidence interval for the difference in the two proportions is written as

Difference in sample proportions ± margin of error

Sample proportion, p= x/n

Where x = number of success

n = number of samples

For the girls,

x = 60

n1 = 80

p1 = 60/80 = 0.75

For the boys

x = 80

n2 = 120

p2 = 80/120 = 0.67

Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.8 = 0.2

α/2 = 0.2/2 = 0.1

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.1 = 0.9

The z score corresponding to the area on the z table is 1.282. Thus, z score for confidence level of 80% is 1.282

Margin of error = 1.282 × √[0.75(1 - 0.75)/80 + 0.67(1 - 0.67)/120]

= 1.282 × √0.00418625

= 0.081

Confidence interval = 0.75 - 0.67 ± 0.081

= 0.08 ± 0.081

b) The formula for determining the standard error of the distribution of differences in sample proportions is expressed as

Standard error = √{(p1 - p2)/[(p1(1 - p1)/n1) + p2(1 - p2)/n2}

Therefore,

Standard error = √{(0.

75 - 0.67)/[0.75(1 - 0.75)/80 + 0.67(1 - 0.67)/120]

Standard error = √0.08/0.00418625

Standard error = 4.37

c) the difference in the probability between that girls prefer math more and boys prefer math more is

0.75 - 0.67 = 0.08

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

whats the question?

step-by-step explanation: