A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained physical activity. What sample size should be obtained the wishes the estimate to be within three percentage points
with 90% confidence, assuming that
(a) he uses the estimates of 21.3% male and 19.5% female from a previous year?
(b) he does not use any prior estimates?
(a)n (Round up to the nearest whole number)
(b) (Round up to the nearest whole number.)
Using the z-distribution and the formula for the margin of error, it is found that:
a) A sample size of 54 is needed.
b) A sample size of 752 is needed.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so [tex]z = 1.645[/tex].
Item a:
The estimate is [tex]\pi = 0.213 - 0.195 = 0.018[/tex].
The sample size is n for which M = 0.03, hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.018(0.982)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.018(0.982)}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.018(0.982)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.018(0.982)}}{0.03}\right)^2[/tex]
[tex]n = 53.1[/tex]
Rounding up, a sample size of 54 is needed.
Item b:
No prior estimate, hence [tex]\pi = 0.05[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.5(0.5)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]
[tex]n = 751.7[/tex]
Rounding up, a sample of 752 should be taken.
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Help me with this pls
Answer:
Step-by-step explanation:
lin ran 4 laps around the track in 5 minutes, if lin ran 21 laps, how long does it take her
Answer:
26 1/4 minutes or 1635 seconds
Step-by-step explanation:
Lin runs 4 laps in 5 minutes. You must turn this into a unit rate. In order to do this, you divide 4 laps by 4 to get 1 lap. To get the equivalent, you also have to divide 5 minutes (300 seconds) by 4. This will get you one lap for every 75 seconds. Because Lin ran 21 laps, see how many times 4 can go into 20 using a remainder if necessary. 4 can go into 21 5 times with a remainder of 1. 4*5=20 5*5=25. Now you add 75 seconds because you have an extra lap.
Determine a7 when a1 = - 4, r = 2
Answer:Geometric Sequence: an=a1rn−1. Explanation: a6=7×2(6−1)=7×32=224. hope that helped.
Step-by-step explanation:
Please I need help fast
Answer:
55
Step-by-step explanation:
Combine both bases (15+7 = 22)
Divide by 2 (22/2 = 11)
Multiply by height (11 x 5 = 55)
The temperature at the North Pole averages -36࿁F. This past winter, the temperature averaged -47࿁F. Write a correct statement that compares the absolute values of the two temperatures
Comparing the temperature average, it can be concluded that the current average temperature is higher than the past average by 11°F
The temperature difference between the present and past winter can be expressed thus :
Current temperature average = - 36°F Past average = - 47°FTemperature difference :
-36 - (-47) = 11°FTherefore, we can conclude that the current average temperature is higher than the past average by 11°F
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For every 3 minutes that Ginny plays on the computer, she plays outside for 10 minutes. What is the ratio of minutes Ginny plays on the computer to minutes she plays outside?
Three to Ten 3:10
...................................................
OMG HELP RN
Sarah climbed 3,600 feet of the way up Pikes Peak and then stopped to rest. After she stops, she continues to climb at a rate of 85 feet per hour for h hours. Which expression indicates her elevation, in feet, h hours after she stops?
A.
3,600 ÷ 85 × h
B.
3,600 + 85 × h
C.
(3,600 + 85) ÷ h
D.
3,600 - 85 × h
Answer: the answer is d hope this helps if not i'm sorry
Find the equation of the exponential function represented by the table below:
x y
0 5
1 15
2 45
3 135
y=
Answer:
y=5·3x
Step-by-step explanation:
x=0, y=5:
5=a·b↑0 a=5
x=1, y=15:
15=5·b↑1
b=15/5=3
The equation of the exponential function is y = 5(3)ˣ
What is an exponential function?An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
Given,
x: 0, 1, 2, 3
y: 5, 15, 45, 135
We have to find the exponential equation:
The exponential function in the form:
y = a × b ˣ
y value of x as 0 is 5.
This is the a value in the equation.
The ratio of values between x as 1 and x as 0 is 15/5 which is equal to 3. This is the value of b in the equation.
Therefore, the equation will become:
y = 5 × 3 ˣ
Hence the equation of the exponential function is y = 5(3)ˣ
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A solid right square prism is cut into 4 equal pieces parallel to its bases. The
volume of each piece is V = 1/4s2h.Solve the formula for s
Answer:
Step-by-step explanation:
If the volume of each piece is V = 1/4s²h then formula for s is 2√V/h
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that a solid right square prism is cut into 4 equal pieces parallel to its bases
The volume of each piece is V = 1/4s²h.
We have to solve for s
4V/h=s²
Take square root on both sides
√4V/h = s
2√V/h = s
Hence, if the volume of each piece is V = 1/4s²h then formula for s is 2√V/h
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f(x)=ax^2 +bx +c solve: heigh 275 width 290
Answer:
800 i think
Step-by-step explanation:
1+×= ???? answer it
Answer:
1+x=x
Step-by-step explanation:
1 is only one letter
Please help questions is down below.
Please answer all!
No bots pls!!!!!! Ill give brain thing
WILL GIVE 100PTS
Find the slope of a line that passes through (-2, -3) and (1, 1).
A. 1 /3
B. 1
C. 2
D. 4/3
Answer:
D
Step-by-step explanation:
Y2-Y1/x2-x-1
Answer:
D
Step-by-step explanation:
Formula for slope is (y2-y1)/(x2-x1).
(1-(-3))/(1-(-2)) = 4/3
Micah earns 2 points for every 3 questions he answers correctly on a test. If he answered 24 questions correctly, how many points did he earn?
Answer:
16 points.
Step-by-step explanation:
24*2/3 = 16.
Hope this helped!
*Sorry if I'm wrong, though I think I'm correct.*
Enjoy the rest of your day.
Answer:16
Step-by-step explanation: 24 divided by 3 because it is for every 3 questions. You get 8. He gets 2 points for every 3 questions so 8 times 2 is 16.
Help help help help help help
Answer:
Step-by-step explanation:
A' = (-1 + 4, 2 + 6) = (3, 8)
B' = (-2 + 4, -3 + 6) = (2, 3)
A' = (-5 + 4, -1 + 6) = (-1, 5)
Evaluate. (w^2/x -3) ÷10 × z when w= -4, x = 0.8, and z = -4/5 Enter your answer as a simplified mixed number in the box.
Answer:
-1.36
Step-by-step explanation:
(-4^2/0.8-3)/10×-4/5=-1.36
Use logarithms to find the exact solution for 7(17^−9)−7=49.
please answer fully ?/'//////////////////////
Answer:
17.5
Step-by-step explanation:
i solved it and got that answer. hope this helps =)
Find the slope of the line that contains the following pair of points:
(4,-5) and (-1, -3).
Step-by-step explanation:
slope is y2-y1/x2-x1
-3-4=-7
-1-4=-5
now that you have -7/-5, or negative seven fifths, simplify.
you get -0.4, or -2/5 as your slope
Hope this helps!!
-2.875 greater than or less than -2 7/8
Answer:
They are both the same.
Step-by-step explanation:
-2.875
7/8 = 0.875 thus -2 7/8 is equal to -2.875
math question!!!!!!!!!!!
Answer:
A: Walking
Step-by-step explanation:
-It cannot be biking because the constant of proportionality (COP) is 9.5 miles (per hour).
-It cannot be running because the COP is 5 miles (per hour).
-It cannot be swimming because the COP is 4.5 miles (per hour).
he is walking
14 divided by 4 is equivalent to 3.5 the equation being 14/4=3.5 or 3 1/2
1.7 6/5
2.4 25/25
3.28/3
what is the lowest term?
Answer:
3.
[tex] \frac{28}{3} [/tex]
Step-by-step explanation:
number 1 equals 8 1/5
number 2 equals 5
number 3 equals 9 1/3
Janelys buys milk and apples at the store.
• She pays a total of $41.22.
• She pays a total of $3.22 for the milk.
• She buys 8 bags of apples that each cost the same amount.
.
Write and solve an equation which can be used to determine x, how much each bag
of apples costs.
Answer:
Each bag costs $4.75
Step-by-step explanation:
41.22 = 3.22 + 8x
38 = 8x
4.75 = x
If an item that originally cost $20 is increased to $27, what is the percentage of increase in the item?
These tables of ordered pairs represent some points on the graphs of lines s and t.
Which system of equations is represented by lines s and t?
5x−2y=−157x+4y=20
3x+5y=−185x−9y=25
x+4y=−89x−y=21
2x−y=−142x+y=6
The equation of line S is y = 2x + 14 while that of line T is y = -2x + 6.
A linear equation is in the form:
y = mx + b;
where y, x are variables, m is the slope of the line and b is the y intercept.
For line s, using the points: (-5, 4) and (4, 22). Hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-4=\frac{22-4}{4-(-5)} (x-(-5))\\\\y-4=2(x+5)\\\\ y=2x+14[/tex]
Line T passes through the points (-4, 14) and (5, -4). Hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-14=\frac{-4-14}{5-(-4)} (x-(-4))\\\\y-14=-2(x+4)\\\\ y=-2x+6[/tex]
Hence the equation of line S is y = 2x + 14 while that of line T is y = -2x + 6.
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The number of eggs Mia can sell varies directly with the number of chickens she owns. The more hens she owns, the more
eggs she can sell. If she has 38 eggs each week when she owns 6 chickens, then how many eggs will she get if she has 15
chickens?
If there are 15 chickens. Then the number of eggs will be 95.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
The number of hens Mia has directly affected how many eggs she can sell. She can sell more eggs if she has more chickens. If she has 6 hens and produces 38 eggs every week.
Let the number of eggs be x. Then the equation is written as,
x / 15 = 38 / 6
x = 95
If there are 15 chickens. Then the number of eggs will be 95.
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geomtry plz help me 15 pointz
Answer:
m∠R=76°
Step-by-step explanation:
∠STR=∠RST=(2x+2)° (base angles of isos triangle)
2(2x+2)+(3x+1)=180 (angle sum of triangle)
4x+4+3x+1=180
7x+5=180
7x=180-5
=175
x=175÷7
=25
Hence, m∠R = (3x+1)°
= [3(25)+1]°
= (75+1)°
= 76°
Answer:
m∠R=76º
Step-by-step explanation:
All angles in a triangle add up to 180º.
The triangle given is an isosceles triangle.
(2x+2)+(3x+1)+(2x+2)=180
Remove parentheses.
2x+2+3x+1+2x+2=180
Collect like terms.
7x+2+1+2=180
Add.
7x+5=180
Subtract 5 from both sides of the equation.
7x=175
Divide 7 from both sides of the equation.
x=25
m∠R=(3x+1)º
3x25+1=76º
m∠R=76º
Hope this helps :)
BRAINLIEST TO CORRECT PLEASE HURRY
Answer:
-32
Step-by-step explanation:
Are the following polynomial sets open or closed? 6. (x ^ 2 + x - 4) - (x ^ 2 + x + 8) 7 (2 - x)(1 + 3x) 8. (5b - 3c)(7b - 3c)
Answer:
=5880b2x4−6048bcx4+1512c2x4−3920b2x3+4032bcx3−1008c2x3+33320b2x2−34272bcx2+8568c2x2−82320b2x+84672bcx−21168c2x−31360b2+32256bc−8064c2+6x2+6x−24
Step-by-step explanation: