Answer:
a)
The probability that both will be hopelessly romantic is
P(X = 2) = 0.0361
b)
The probability that at least one person is hopelessly romantic is
P( X>1) = 0.3439
Step-by-step explanation:
a)
Given data population proportion 'p' = 19% =0.19
q = 1-p = 1- 0.19 =0.81
Given two people are randomly selected
Given n = 2
Let 'X' be the random variable in binomial distribution
[tex]P(X=r) =n_{C_{r} } p^{r} q^{n-r}[/tex]
The probability that both will be hopelessly romantic is
[tex]P(X= 2) =2_{C_{2} } (0.19)^{2} (0.81)^{2-2}[/tex]
P(X = 2) = 1 × 0.0361
The probability that both will be hopelessly romantic is
P(X = 2) = 0.0361
b)
The probability that at least one person is hopelessly romantic is
P( X>1) = 1-P(x<1)
= 1 - ( p(x =0)
= [tex]1- 2_{C_{0} } (0.19)^{0} (0.81)^{2-0}[/tex]
= 1 - (0.81)²
= 1 -0.6561
= 0.3439
The probability that at least one person is hopelessly romantic is
P( X>1) = 0.3439
What is a plane in mathematical terms
Answer:
Step-by-step explanation:
A plane is a flat, two-dimensional surface that extends infinitely far.
A student walk 60m on a bearing of 028 degree and then 180m due east. How is she from her starting point, correct to the nearest whole number?
Answer:
She is 215 m from the starting point
Step-by-step explanation:
Let's begin by constructing a figurative representation of the information given (figure attached)
We know 2 sides of the triangle and the inner angle, we can therefore use the Cosine Rule
Mathematically represented as:
b² = a² + c² - 2ac(CosB)
b = ?, a = 60 m, c = 180, B = 118° (the sum of the 90° right angle at B + the interior angle of 28° from A)
b² = 60² + 180² - 2(60)(180)Cos 118°
b² = 3600 + 32400 - (- 10140.586)
b² = 46140.586 ⇒ b = [tex]\sqrt{46140.586}[/tex]
b = 214.8 m ≈ 215 m
b = 215 m (to the nearest whole number)
∴ the student is 215 m from the starting point
In a spelling test the scores are 15,8,11,16,10,5and 10. what is the range
Solution,
Given data=15,8,11,16,10,5,10
Highest score= 16
lowest score= 5
Range=highest score- lowest score
=16-5
=11
Answer:
[tex]10[/tex]
Step-by-step explanation:
Given data =
[tex]15 \: \: 8 \: \: 11 \: \: 16 \: \: 10 \: \: 5 \: \: 10[/tex]
[tex]range = height \: \: - \: lowest \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: score \: \: \: \: \: \: \: \: \: \: \: \: \: score \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 15 \: \: \: \: \: - \: \: \: \: 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 10[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
0.09 is smaller than 0.001
Answer:
no
Step-by-step explanation:
A car is traveling 80 KM in an hour how many minutes will it take to go from Miami to key largo
84.5 minutes reeeeeee
The car will take 84 minutes to go from Miami to Key Largo.
Given that, speed=80 km/hour and distance = 70 miles.
What is the speed of a object?Speed is the rate at which an object's position changes, measured in meters per second. The equation for speed is simple: distance divided by time.
Now, convert miles to kilometres. We know that 1 mile=1.6 kilometre.
That is 70 miles =70×1.6 =112 km
Then, Time=Distance/Speed
⇒Time =112/80=1.4 hours
So, 1.4 hours=60×1.4=84 minutes
Therefore, the car will take 84 minutes to go from Miami to Key Largo.
To learn more about the speed visit:
https://brainly.com/question/7359669.
#SPJ2
Your question is incomplete, probably the complete question/missing part is:
A car is travelling 80 KM in an hour how many minutes will it take to go from Miami to key largo? (70 miles)
There are 13 comma 17913,179 eligible voters in one town. In a poll of 834834 eligible voters from this town, the proportion who say that they plan to vote in the next mayoral election is 0.470.47. Based on that sample statistic, what is the best estimate of the proportion for all eligible voters in the town? Round to two decimal places as needed.
Answer:
The best estimate of the proportion for all eligible voters in the town, that is, the best estimate for the population, is 0.47.
Step-by-step explanation:
Since the sample is large enough, the proportion from the sample is the best estimate for the proportion of the population.
In this question, we have that:
For the sample, the proportion who say that they plan to vote in the next mayoral election is 0.47
So the best estimate of the proportion for all eligible voters in the town, that is, the best estimate for the population, is 0.47.
An item is regularly priced at $80. Chau bought it on sale for 15% off the regular price. How much did Chau pay?
only $68...steps.... (80*15% =12 /80-12=68
An urn contains 5 are red balls and 6 blue balls. Suppose 5 are randomly selected without replacement. What is the probability that exactly 3 are red? Answer correct to four decimal places.
Answer:
27.94%
Step-by-step explanation:
The statement tells us that we have 5 red balls and 6 blue balls, that is, there are 11 in total (5 + 6)
So the probability of red balls = 5/11 and blue balls probability = 6/11
Let X be the number of red balls of those 5 selected balls.
Then X follows a binomial distribution with the following parameters:
n = 5
p = 5/11
q = 6/11
P (X) = nCx * p ^ (x) * q ^ (n -x)
required probability is P (X = 3), replacing:
P (X = 3) = 5C3 * (5/11) ^ (3) * (6/11) ^ (5 -3)
P (X = 3) = 5! / (3! (5-3)!) * 0.02794
P (X = 3) = 10 * 0.02794
P (X = 3) = 0.2794
Which means that the probability is 27.94%
The degree of the polynomial f (x) is 3, and the degree of the polynomial g(x) is 4. Find the degree of the polynomial f (x) + g(x).
Answer:
The degree would be 4
Step-by-step explanation:
When you add polynomials without multiplying bases, you cannot add or subtract the degree. So the highest degree would be 4 in this case.
The temperatures at several times of the day are shown in the coordinate plane below. The x-axis represents the number of hours before or after noon. For example, -1 would represent 11 a.m. The y-axis represents the temperature in degrees Celsius. At 5 p.m.5, start text, space, p, point, m, point, end text, the temperature is halfway between the temperature at 2 \text{ p.m.}2 p.m.2, start text, space, p, point, m, point, end text and the temperature at 8 \text{ p.m.}8 p.m.8, start text, space, p, point, m, point, end text What coordinates represent the temperature at 5pm?
Question:
The temperatures at several times of the day are shown in the coordinate plane below. The x-axis represents the number of hours before or afternoon. For example, -1 would represent 11 a.m. The y-axis represents the temperature in degrees Celsius.At 5 p.m, the temperature is halfway between the temperature at 2 p.m. and the temperature at 8 p.m.
What coordinates represent the temperature at 5 p.m.?
Answer:
(5, 2)
=> At 5pm, the temperature is at 2⁰C
Step-by-step Explanation:
Coordinates of any point on a cartesian/coordinate plane is represented by (x, y). Where x is the number at the point on z-axis, while y is the number at the same point on the y-axis.
From the diagram of the coordinate plane attached below, we can simply find out what coordinates represent the temperature at 5pm.
==> Given that the temperature at 5pm is half way between the temperature at 2pm (y=7) and temperature at 8pm (y=-3), the point that is being referred to = [7+(-3)] ÷ 2 = ⁴/2 = 2 (i.e. 2 on the y axis representing temperature)
*The position of the point is indicated in the second picture that is attached below.
At that position of the point, we have 2 as the coordinate for the y axis representing temperature, and at that same position, we have 5 on the x-axis representing the number of hours.
Therefore, coordinates of the point (x, y) representing 5p.m = (5, 2)
==> At 5pm, the temperature is at 2⁰C
Answer:
Look above for a good answer!
Step-by-step explanation:
The coordinates are 5,2
Dr. Dormeur studies sleep and sleep disorders. She is curious as to whether technology exposure before bedtime causes people to fall asleep more slowly. She recruits a sample of 60 middle-aged women from a local church who reported no history of sleep problems. She creates three conditions, and randomly assigns participants to one condition. All participants come to the sleep lab for two nights in a row, the first night with no treatment, the second night with treatment. In the first condition (A), participants were asked to play an online game (Candy Crush) on an iPad for 10 minutes prior to going to bed. In the second condition (B), participants were asked to read an article using an iPad that discussed tricks and tips for improving one’s score on Candy Crush (which took about 10 minutes). In the third condition (C), participants were asked to read a newspaper article about the inventor of Candy Crush (which took about 10 minutes). With the use of an electroencephalograph (EEG), the researcher measures how long it takes participants to fall asleep. Which of the following designs is Dr. Dormeur using?
a. one-way between-subjects ANOVA.b. chi-square test.c. simple linear regression.d. repeated-measures t-test.
Answer:
Dr Domeur is using repeated measures t-test
Step-by-step explanation:
Dr Dormeur is using the repeated measures t test also known as within-subjects design because the design is between participants. Repeated Measures assesses the change in a continuous outcome across time or within-subject.
Dr Domeur makes measurements using only one group of subjects, and the tests on each subject can be repeated more than once after different treatments. From the question, the researcher Dr Domeur uses the same subjects with every condition of the research and the control. Repeated measures are collected in a longitudinal study that assesses change over time.
can some work out 1/(2x10^5)+(5x10^4)
2.
The Parkside Packing Company needs a rectangular shipping box. The box must have a length
of 11 inches and a width of 8 inches. Find, to the nearest tenth of an inch, the minimum height
of the box such that the volume is at least 800 cubic inches.
(3 points)
Answer:
9.1 Inches
Step-by-step explanation:
Length of the proposed box=11 Inches
Width of the proposed box=8 Inches
Required Volume, [tex]V \geq 800 $ cubic inches.[/tex]
Volume of a Rectangular Prism =Length X Width X Height
Therefore:
[tex]800\\11*8*Height\geq 800\\88*Height \geq 800\\$Divide both sides by 88\\Height \geq 800 \div 88\\Height \geq 9.\overline{09}$ inches[/tex]
Therefore, the minimum height to the nearest tenth of an inch is 9.1 Inches.
A philosophy professor assigns letter grades on a test according to the following scheme. A: Top 13% of scores B: Scores below the top 13% and above the bottom 55% C: Scores below the top 45% and above the bottom 23% D: Scores below the top 77% and above the bottom 9% F: Bottom 9% of scores Scores on the test are normally distributed with a mean of 76 and a standard deviation of 7.9. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.
Answer:
The minimum score required for an A grade is 85.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 76, \sigma = 7.9[/tex]
Find the minimum score required for an A grade.
The top 13% of the scores are A, so the minimum is the 100-13 = 87th percentile, which is X when Z has a pvalue of 0.87. So X when Z = 1.127.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.127 = \frac{X - 76}{7.9}[/tex]
[tex]X - 76 = 7.9*1.127[/tex]
[tex]X = 84.9[/tex]
Rounding to the nearest whole number:
The minimum score required for an A grade is 85.
Consider the differential equation y '' − 2y ' + 5y = 0; ex cos(2x), ex sin(2x), (−[infinity], [infinity]). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. The functions satisfy the differential equation and are linearly independent since W(ex cos(2x), ex sin(2x)
Answer:
Step-by-step explanation:
Characteristic equation:
[tex]\lambda^2-2\lambda + 5 =0[/tex]
[tex]\lambda = 1\pm2i[/tex]
The solution of the ODE is
[tex]y = e^x(C_1 cos(2x) + C_2 sin(2x) )[/tex]
Now, very find by taking the first and the second derivative of y.
[tex]y' = e^x(-2 C_1 sin (2x) +2C_2 cos (2x)) +e^x (C_1 cos (2x) + C_2sin(2x))[/tex]
[tex]=-2e^xC_1 sin(2x) +2e^xC_2 cos (2x)+C_1e^xcos(2x) + C_2e^x sin(2x)[/tex]
[tex]y" = -2e^x C_1 sin(2x) -4e^x C_1cos(2x)+2e^xC_2cos(2x)-4e^xC_2sin(2x) +C_1e^x cos(2x) -2C_1e^xsin(2x)+C_2e^x sin(2x) +2C_2e^x cos(2x)[/tex]
[tex]=-4C_1e^xsin(2x) -3C_1e^x cos(2x) +4C_2e^xcos(2x) -3C_2e^xsin(2x)[/tex]
Now, put all in y" -2y'+5y and consider if it = 0 or not.
A juggler perform in a telant contest. He is given 10 marks by each of the 4 judges. What’s his total score?
Answer:
40
Step-by-step explanation:
The answer is 40. There are 4 judges, and each gave him a 10. This can be shown by an equation.
1. 4 * 10 = total score
2. 40 = total score.
Hope this helps! (Please consider giving brainliest)
Answer:
40 marks
Step-by-step explanation:
Since each judge gives him 10 marks each, then we get:
10 marks × 4 judges = 40 marks
His total score is 40 marks.
Jane has a pre-paid cell phone with NextFell. She can't remember the exact costs, but her plan has a monthly fee and a charge for each minute of calling time. In June she used 370 minutes and the cost was $133.00. In July she used 530 minutes and the cost was $181.00.
A) Express the monthly cost C
C
in terms of x
x
, the number of minutes of calling time she used.
Answer: c
B) If Jane used 477 minutes of calling time in August, how much was her bill?
Answer: $
Answer:
C = 0.30x +22$165.10Step-by-step explanation:
A) Let x represent minutes used, and C represent monthly charge. We are given two (x, C) pairs: (370, 133.00) and (530, 181.00)
We can use these in the 2-point form of the equation for a line.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
C = (181 -133)/(530 -370)(x -370) +133
C = 48/160(x -370) +133
C = 0.30x -111 +133
C = 0.30x +22
__
B) For x = 477 minutes, the charge will be ...
C = 0.30(477) +22 = $165.10 . . . . for 477 minutes
The monthly cost C = $22 + $0.30x
Jane's bill for August is $165.10
The total amount Jane pays is the sum of the monthly fee and the charge per minute.
Total amount = monthly fee + charge per minute
Two equations can be derived from the question
a + 370b = 133 equation 1
a + 530b = 181 equation 2
Where:
a = monthly fee
b = charge per minute
This equation would be solved using simultaneous equation
Subtract equation 1 from equation 2
160b = 48
Divide both sides of the equation by 160
b = 48 / 160
b = 0.30
Substitute for b in equation 1
a + 370(0.30) = 133
a + 111 = 133
a = 133 - 111
a = 22
Based on the above calculations, the monthly fee is $22 and the charge per minute is $0.30
Equation for monthly cost = $22 + $0.30x
If Jane used 477 minutes, total charge :
$22 + $0.30(477) =
22 + 143.10
= $165.10
A similar question was solved here: https://brainly.com/question/17911105?referrer=searchResults
Several employees have submitted different methods of assembling a subassembly. Sample data for each method are: Minutes Required for Assembly Sample Number Lind's Method Szabo's Method Carl's Method Manley's Method 1 16.6 22.4 31.4 18.4 2 17.0 21.5 33.4 19.6 3 16.9 22.6 30.1 17.6 How many treatments are there?
Answer:
There are 4 treatments
Step-by-step explanation:
In this study, there are four treatments. Each sample from 1 to 3 was subjected to each treatments which in this case are the methods; Lind's Method, Szabo's Method, Carl's Method and Manley's Method.
Thus, the methods in this study are the treatments the samples are subjected to.
2 Points
Suppose you buy 6 buckets of apples and 4 buckets of peaches for $42. If
you bought 8 buckets of apples and 2 buckets of peaches, you would have
spent $36. How much is one bucket of apples (a), and one bucket of peaches
(p)?
A. a = $3, p = $6
B. a = $8, p = $2
C. a = $6, p = $4
D. a = $6, p = $3
SUBMIT
Answer:
A. a = $3, p = $6
Step-by-step explanation:
Let the cost of a bucket of apple=a
Let the cost of a bucket of peaches=p
6 buckets of apples and 4 buckets of peaches costs $42.
6a+4p=428 buckets of apples and 2 buckets of peaches costs $36.
8a+2p=36 (Multiply by 2 to make the coefficient of p 4)16a+4p=72We solve the two resulting equations simultaneously
6a+4p=42
16a+4p=72
Subtract
-10a=-30
Divide both sides by -10
a=$3
Next, we substitute a=$3 in any of the equation to solve for p
6a+4p=42
6(3)+4p=42
4p=42-6(3)
4p=42-18
4p=24
Divide both sides by 4
p=$6
Therefore, a bucket of apple costs $3 and a bucket of peaches costs $6.
A homeowner is designing a rectangular pool for her backyard. Due to the size of the yard, the width of the pool will be one-third its length, and the pool will have a uniform depth of 5 feet. Which of the following equations can be used to describe l, the length of the pool, in terms of its volume, V?
Answer:
Step-by-step explanation:
Which of the following is an arithmetic sequence?
Answer: choice D
Step-by-step explanation:
An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
in this exampke the constant(d) is -3
Answer:
D is the correct answer.
Step-by-step explanation:
because the numbers are decreased by -3
Defination: in arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
g(x) = x-6
Domain of g:
Answer:
All real numbers
Step-by-step explanation:
The domain is just what values of x you can plug in as an input. In this case, you can plug in any number, as the graph is just a line that has no restrictions. An example of a case where the domain isnt just any number would be g(x) = 5/x, because in that case, x couldn't be 0 because you cant divide by zero.
Answer: all real numbers
Step-by-step explanation:
what is the measure of p?
A.39
B.56
c.
C.29
D.97
Answer:
The correct answer is c. 29
Step-by-step explanation:
Hope it works out , brainliest appreciated !!A loan company charges $30 interest
for a one month loan of $500. Find the annual interest they are charging
Answer:
0.72%
Step-by-step explanation:
Finding what percentage is $30 of $500:
30/500 x 100 = 6
So, it is 5% per month.
Converting it to annual:
6% x 12 = 0.72%
The annual interest they are charging is $360.
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money.
Now it is given that,
Amount of interest charged = $30
Amount of loan = $500
Duration = 1 month
Now since 1 year = 12 month
Thus, Amount of interest charged in 1 year = 12 * $30
⇒ Amount of interest charged in 1 year = $360
this is the amount they are charging annually.
Thus, the annual interest they are charging is $360.
To learn more about interest :
https://brainly.com/question/14724009
#SPJ2
n a survey of 331 customers, 66 say that service is poor. You select two customers without replacement to get more information on their satisfaction. What is the probability that both say service is poor?
Answer:
3.93% probability that both say service is poor
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The customers are chosen without replacement, and the order in which they are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
What is the probability that both say service is poor?
Desired outcomes:
Two saying it is poor, from a set of 66. So
[tex]D = C_{66,2} = \frac{66!}{2!(66-2)!} = 2145[/tex]
Total outcomes:
Two customers from a set of 331. So
[tex]T = C_{331,2} = \frac{331!}{2!(331-2)!} = 54615[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{2145}{54615} = 0.0393[/tex]
3.93% probability that both say service is poor
What is (-3)x(5-7)-9(39/3)
Answer:-111
Step-by-step explanation:
PLEASE HELP!!! WILL GIVE BRAINLIEST!!!
Answer:
1. Reason = Angles forming a linear pair sum to 180
2. Step = m<QTR+ m<RTS = 180
3. reason = transitive property of equality
4. step = m<PTQ = m<RTS. reason = subtraction property of equality
uppose that Mary's utility function is U(W) = W0.5, where W is wealth. She has an initial wealth of $100. How much of a risk premium would she want to participate in a gamble that has a 50% probability of raising her wealth to $115 and a 50% probability of lowering her wealth to $77? Mary's risk premium is $ nothing. (round your answer to two decimal places)
Note that [tex]U(W) = W^{0.5}[/tex]
Answer:
Mary's risk premium is $0.9375
Step-by-step explanation:
Mary's utility function, [tex]U(W) = W^{0.5}[/tex]
Mary's initial wealth = $100
The gamble has a 50% probability of raising her wealth to $115 and a 50% probability of lowering it to $77
Expected wealth of Mary, [tex]E_w[/tex]
[tex]E_{w}[/tex] = (0.5 * $115) + (0.5 * $77)
[tex]E_{w}[/tex] = 57.5 + 38.5
[tex]E_{w}[/tex] = $96
The expected value of Mary's wealth is $96
Calculate the expected utility (EU) of Mary:-
[tex]E_u = [0.5 * U(115)] + [0.5 * U(77)]\\E_u = [0.5 * 115^{0.5}] + [0.5 * 77^{0.5}]\\E_u = 5.36 + 4.39\\E_u = \$ 9.75[/tex]
The expected utility of Mary is $9.75
Mary will be willing to pay an amount P as risk premium to avoid taking the risk, where
U(EW - P) is equal to Mary's expected utility from the risky gamble.
U(EW - P) = EU
U(94 - P) = 9.63
Square root (94 - P) = 9.63
If Mary's risk premium is P, the expected utility will be given by the formula:
[tex]E_{u} = U(E_{w} - P)\\E_{u} = U(96 - P)\\E_u = (96 - P)^{0.5}\\(E_u)^2 = 96 - P\\ 9.75^2 = 96 - P\\95.0625 = 96 - P\\P = 96 - 95.0625\\P = 0.9375[/tex]
Mary's risk premium is $0.9375
can someone please help me!
Answer:
D
Step-by-step explanation:
Let's derive the equations for the two graphs;
For the graph towards the right,
The slope = y2-y1/x2-x1; so we choose two corresponding points (x1,y1); (x2,y2)
Let's choose points;
(2,1) and (3,2)
The slope = 2-1/ 3-2 = 1/1 = 1
From the general equation of a line
y = mx + c = 1× x + (-1) = x-1
y = x-1
Similarly for that towards the left we have;
The slope = y2-y1/x2-x1; so we choose two corresponding points (x1,y1); (x2,y2)
Let's choose points;
(2,1) and (3,2)
The slope = 2-1/ 3-2 = 1/1 = 1
From the general equation of a line
y = mx + c = 1× x + (-1) = x-1
y = x-1
Similarly for that towards the left we have;
The slope = y2-y1/x2-x1; so we choose two corresponding points (x1,y1); (x2,y2)
Let's choose points;
(-7,0) and (-4,-3)
Slope = -3-0/ -4-(-7) = -3/ 3 = -1
From the general equation of a line
y = mx + c = -1× x + c = -x + c
Since c is not obvious we can find the equation by picking just a point along the graph along side an arbitrary (x,y) point hence we have for slope;
If we pick (-7,0)
y-0 / x-(-7) = -1
y / x+7 = -1
y = -x -7
The equations of the graphed lines are;
y=x-1
y=-x-7
Look at option D you we see it's the same as the equation of the graph towards the right y=x-1
For the records
y=[x+3]-4 = x+3-4 = x-1
Hypertension is when an adult is classified as having high blood pressure (above 130 systolic blood pressure is considered hypertension). Researchers want to know the proportion of adult North Americans (above age of 18) that have hypertension. Based on a study of 3532 adult North Americans, 1219 of them were classified as having hypertension.
a. Researchers want to test if more than a quarter of all North American adults have hypertension (that is to say more than 25% proportion of North American adults). State the null and alternative hypothesis in proper notation.
b. Create a 95% confidence interval for the true proportion of adult North Americans that have hypertension. Interpret this interval in context of the study.c. Say your 95% confidence interval is (0.329 , 0.361). Can you say with a high degree of confidence that more than a quarter of all North Americans have hypertension. Explain in a sentence or two.
d. If we were to decrease our level of confidence, what would we expect to happen to the confidence interval? Get wider/ get narrower/ stay the same ?
Answer:
Step-by-step explanation:
a) We would set up the hypothesis test.
For the null hypothesis,
H0 : p ≥ 0.25
For the alternative hypothesis,
H1 : p < 0.25
b) from the given information,the sample proportion or point estimate for the population proportion is
1219/3532 = 0.35
Confidence interval = sample proportion ± margin of error
Margin of error = z × √pq/n
p = 0.35
q = 1 - 0.35 = 0.65
z score for 95% confidence level is 1.96
Margin of error = 1.96 × √(0.35 × 0.65)/3532 = 0.016
Confidence interval = 0.35 ± 0.016
c) Given that the 95% confidence interval is (0.329 , 0.361), it means that the lower limit of the confidence interval is 0.329 and the upper limit is 0.361
If more than a quarter of all North Americans have hypertension. It means that the true proportion can be within this interval. 95% confidence interval is a high degree of confidence. Therefore, we can say that with a high degree of confidence that more than a quarter of all North Americans have hypertension.
d) it would get narrower
