Use the distance formula and the Pythagorean theorem to find the distance,to the nearest tenth,between each pair of points

A College Alcohol Study has interviewed random samples of students at four-year colleges. In the most recent study, 494 of 1000

Vinil7 [7]

Answer:

The 95% confidence interval for the difference between the proportion of women who drink alcohol and the proportion of men who drink alcohol is (-0.102, -0.014) or (-10.2%, -1.4%).

Step-by-step explanation:

We want to calculate the bounds of a 95% confidence interval of the difference between proportions.

For a 95% CI, the critical value for z is z=1.96.

The sample 1 (women), of size n1=1000 has a proportion of p1=0.494.

$p_1=X_1/n_1=494/1000=0.494$

The sample 2 (men), of size n2=1000 has a proportion of p2=0.552.

$p_2=X_2/n_2=552/1000=0.552$

The difference between proportions is (p1-p2)=-0.058.

$p_d=p_1-p_2=0.494-0.552=-0.058$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{494+552}{1000+1000}=\dfrac{1046}{2000}=0.523$

The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.523*0.477}{1000}+\dfrac{0.523*0.477}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.000249+0.000249}=\sqrt{0.000499}=0.022$

Then, the margin of error is:

$MOE=z \cdot s_{p1-p2}=1.96\cdot 0.022=0.0438$

Then, the lower and upper bounds of the confidence interval are:

$LL=(p_1-p_2)-z\cdot s_{p1-p2} = -0.058-0.0438=-0.102\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= -0.058+0.0438=-0.014$

The 95% confidence interval for the difference between proportions is (-0.102, -0.014).

7 0

3 years ago

HELP PLEASE!!!! 8TH GRADE MATH

vladimir2022 [97]

1. 12 pages per minute

3 0

3 years ago

Combine the like terms to create an equivalent expression:<br> -2x-x+8

lara31 [8.8K]

Answer:

-3x+8

Step-by-step explanation:

-2x-x+8=

-3x+8

7 0

3 years ago

in a triangle TRY measure angle R is 3 times measure angle T and measure angle Y is 15 more than measure angle T find the measur

r-ruslan [8.4K]

Answer:

Angle R is 99 degree

Angle Y=48 degrees

Angle T is 33 degrees

Step-by-step explanation:

Let angle T be x

Angle R will be 3x

Angle Y will be x+15

Total=x+3x+x+15=5x+15

5x+15=180

5x=165

x=165/5=33

Therefore, angle T is 33 degrees, angle Y=15+33=48 degrees and angle R=33*3=99 degrees

5 0

3 years ago

PLEASE SHOW YOUR WORK.

schepotkina [342]

Answer:

a) Shawn's error was that he Multiplied 15 by 2x only. He didn't Multiply 15 by 7

b) The difference, in square feet, between the actual area of Shawn’s garden and the area found using his expression is given as

98 square feet

Step-by-step explanation:

The area in, square feet, of Shawn’s garden is found be calculating 15(2x + 7). Shawn incorrectly says the area can also be found using the expression 30x + 7.

The correct area =

15(2x + 7).

= 30x + 105 square feet

The error in Shawn’s expression is

= 15(2x + 7)

= 30x + 7 square feet

Shawn's error was that he Multiplied 15 by 2x only. He didn't Multiply 15 by 7

The difference, in square feet, between the actual area of Shawn’s garden and the area found using his expression is given as

30x + 105 square feet - 30x + 7 square feet

= 30x + 105 - (30x + 7)

= 30x - 30x + 105 - 7

= 98 square feet

7 0

2 years ago