Autism and Maternal Antidepressant Use A recent study41 compared 298 children with Autism Spectrum Disorder to 1507 randomly selected con- trol children without the disorder. Of the children with autism, 20 of the mothers had used antidepres- sant drugs during the year before pregnancy or the first trimester of pregnancy. Of the control children, 50 of the mothers had used the drugs.
(a) Is there a significant association between prena- tal exposure to antidepressant medicine and the risk of autism? Test whether the results are sig- nificant at the 5% level.
(b) Can we conclude that prenatal exposure to antidepressant medicine increases the risk of autism in the child? Why or why not?
Answers
Answer:
(a) We conclude that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism at 5% significance level.
(b) Yes, we can conclude that prenatal exposure to antidepressant medicine increases the risk of autism in the child.
Step-by-step explanation:
We are given that Autism and Maternal Antidepressant Use A recent study 41 compared 298 children with Autism Spectrum Disorder to 1507 randomly selected control children without the disorder.
Of the children with autism, 20 of the mothers had used antidepressant drugs. Of the control children, 50 of the mothers had used the drugs.
Let \(p_1\) = proportion of mothers who had used drugs having Autism Spectrum Disorder in their children.
\(p_2\) = proportion of mothers who had used drugs not having Autism Spectrum Disorder in their children.
(a) Null Hypothesis, \(H_0\) : \(p_1=p_2\) {means that there is no significant association between prenatal exposure to antidepressant medicine and the risk of autism}
Alternate Hypothesis, \(H_A\) : \(p_1\neq p_2\) {means that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism}
The test statistics that would be used here Two-sample z test for proportions;
T.S. = \(\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }\) ~ N(0,1)
where, \(\hat p_1\) = sample proportion of mothers who had used drugs having Autism Spectrum Disorder in their children = \(\frac{20}{298}\) = 0.067
\(\hat p_2\) = sample proportion of mothers who had used drugs not having Autism Spectrum Disorder in their children = \(\frac{50}{1507}\) = 0.033
\(n_1\) = sample of children with Autism Spectrum Disorder = 298
\(n_2\) = sample of children without Autism Spectrum Disorder = 1507
So, the test statistics = \(\frac{(0.067-0.033)-(0)}{\sqrt{\frac{0.067(1-0.067)}{298}+\frac{0.033(1-0.033)}{1507} } }\)
= 2.281
The value of z test statistics is 2.281.
Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.
Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism.
(b) Yes, we can conclude that prenatal exposure to antidepressant medicine increases the risk of autism in the child because if we reconsider our hypothesis for one-tailed test in which the null hypothesis states that the prenatal exposure to antidepressant medicine does not increases the risk of autism in the child.
For this hypothesis also, our test statistics will be more than the critical value of z and due to which we reject our null hypothesis and conclude that prenatal exposure to antidepressant medicine increases the risk of autism.
Related Questions
If four loaves of bread costs $8, a loaf of bread and a bag of oranges costs $5, and a loaf of bread, two bags of oranges and a basket of apples costs $12, what is the cost of a basket of apples?
Answers
Answer:
$6
Step-by-step explanation:
4 loaves of bread ---- $8
1 loaf of bread ---- $8 ÷ 4 = $2
one bag of oranges --- $5 - $2 = $3
two bags of oranges --- $3 × 2 = $6
one basket of apples --- $12 - $6 = $6
The cost of a basket of apples is $6.
Please help, I will give brain list.
Answers
Answer:
12.25
Step-by-step explanation:
3.5*3.5=12.25
Answer:
12.25m^2
Step-by-step explanation:
3 1/2 × 3 1/2
3 1/2 is equivalent to 7/2
7/2 × 7/2= 49/4
this simplifies to 12.25
answer: 12.25 m^2
Find the maximum value of √3+ cosx as well as the corresponding value of x where - 360 ≤ x ≤360 which produces the maximun value.
Answers
The maximum value of √3 + cos(x) is 2 and the corresponding value of x that produces the maximum value is x = 0°.
How to find a maximum value?To find the maximum value of √3 + cos(x) and the corresponding value of x that produces the maximum value, we can use the identity cos(x) = √(1 - sin^2(x)). We know that |sin(x)| ≤ 1 for all values of x, so
√3 + cos(x) = √3 + √(1 - sin^2(x)) ≤ √3 + √1 = 2.
Thus, the maximum value of √3 + cos(x) is 2. This maximum value is achieved when cos(x) = 1, or when x = 2nπ (where n is an integer) and sin(x) = 0.
In the range -360° to 360°, the value of x that produces the maximum value of √3 + cos(x) is x = 0°.
So, the maximum value of √3 + cos(x) is 2 and the corresponding value of x that produces the maximum value is x = 0°.
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Terri buys five and seven-eighths ounces of chocolate chips. She uses four and four-sixths ounces in a recipe. How many ounces of chocolate chips does she have left?
Answers
Answer:
1 5/24 ounces--------------------------
Find the difference of the initial and used amounts:
5 7/8 - 4 4/6 = 5 - 4 + 7/8 - 4/6 = Combine whole and fraction parts1 + 7/8 - 2/3 = Simplify1 + 21/24 - 16/24 = Common denominator is 241 + 5/24 = Convert to mixed fraction1 5/24Please help I’m completely stuck
Answers
Answer: 8x
Question 2:Answer: 12x - 3y
hope it helps.
The people who live in chicago form a subset of those who rent apartments in chicago
Answers
D. The statement does not make sense because the set of people who live in Chicago also includes home owners which are not part of the set of people who rent apartments in Chicago.
Hope this helps ✌️
Given each set of information, fi d a linear equation
that satisfies he given conditions, if possible. Passes
through (7, 5) and (3, 17)
Answers
The equation of the line is: y = -3x + 26
What is an equation of the line?
An equation of a line is a mathematical expression that represents a straight line in a two-dimensional Cartesian coordinate system. It can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the equation of a line that passes through two given points, we can use the slope-intercept form of the equation:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points. Once we have the slope, we can use one of the points and the slope to find the y-intercept, b, using the equation:
b = y - mx
where (x, y) is one of the given points.
For the given information that the line passes through (7,5) and (3,17), we can find the slope as:
m = (17 - 5)/(3 - 7) = -3
Using the point (7,5) and the slope, we can find the y-intercept, b, as:
5 = -3(7) + b
b = 26
Therefore, the equation of the line is: y = -3x + 26
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Solve for x and show steps . Is the solution extraneous ? Check your work to show how you determined if the solution is extraneous or not
Square 4x-3=5
Answers
The solution of the equation 4x - 3 = 5 is not extraneous .
How to solve an equation?Extraneous solutions are values that we get when solving equations that aren't really solutions to the equation.
Therefore, let's solve the equation to know whether it is extraneous solution.
Hence,
4x - 3 = 5
add 3 to both sides of the equation
4x - 3 + 3 = 5 + 3
4x = 8
divide both sides of the equation by 4
4x / 4 = 8 / 4
x = 2
Therefore, it is not extraneous solution.
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ATMOSPHERIC SCIENCE The troposphere extends from the Earth's surface to a height of 6-12 miles, dependin
on the location and the season. If a plane is flying at an altitude of 5.8 miles, and the troposphere is 8.6 miles deep in
that area, how much higher can the plane go without leaving the troposphere?
Answers
Answer:
2.8 Miles
Step-by-step explanation:
You subract 5.8 from 8.6 to get the answer.
4. The two legs of a right triangle are equal and the square of its hypotenuse is 50. Find the
length of each leg.
Answers
Answer:
\(Opposite = Adjacent= 5\)
Step-by-step explanation:
Given
\(Hypotenuse^2 = 50\)
\(Opposite = Adjacent\)
Required
Find the length of each leg
This is calculated using Pythagoras Theorem
\(Opposite^2 + Adjacent^2 = Hypotenuse^2\)
\(Opposite^2 + Adjacent^2 = 50\)
Represent the opposite and adjacent with x
\(x^2 + x^2= 50\)
\(2x^2 = 50\)
Divide both sides by 2
\(x^2 = 25\)
Take square roots
\(x = 5\)
Hence:
\(Opposite = Adjacent= 5\)
translate the following words into a expression
a number divided by 6
A. x/6
B. 6/x
C. 6x
D. x + 6
Answers
A. X/6
Hope that helps <3 have a nice day
The National Assessment of Educational Progress (NAEP) is a nationwide assessment of students’ proficiency in nine subjects: mathematics, reading, writing, science, the arts, civics, economics, geography, and U.S. history. The main NAEP assessments are conducted annually on samples of students from grades 4, 8, and 12.
In 2002, the reading scores for female students had a mean of 269 with a standard deviation of 33. Assume that these scores are normally distributed with the given mean and standard deviation.
Identify the scores that are three standard deviationsabove and below the mean of the population. For this example, the limits will be 269 ± (33)(3). The lower limit is . The upper limit is . The probability that a female student will have a score between these limits is .
A score of 302 is above the mean. As a result, the percentage of female students with scores below 302 is .
You can infer that 97.72% of the female students have scores above .
Answers
"97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits
To calculate the scores that are three standard deviations above and below the mean, we use the formula:
Lower limit = Mean - (Standard Deviation * 3)
Upper limit = Mean + (Standard Deviation * 3)
Given:
Mean = 269
Standard Deviation = 33
Using the formula, we can calculate the limits:
Lower limit = 269 - (33 * 3) = 269 - 99 = 170
Upper limit = 269 + (33 * 3) = 269 + 99 = 368
Therefore, the lower limit is 170 and the upper limit is 368.
To calculate the probability that a female student will have a score between these limits, we need to find the area under the normal distribution curve between the lower and upper limits. This can be calculated using a standard normal distribution table or calculator.
Since the distribution is assumed to be normal, approximately 99.72% of the scores will fall within three standard deviations from the mean. Therefore, the probability that a female student will have a score between these limits is approximately 99.72%.
For a score of 302, which is above the mean of 269, we can calculate the percentage of female students with scores below 302:
Percentage = (1 - Probability) * 100
= (1 - 0.9972) * 100
= 0.0028 * 100
= 0.28%
Therefore, approximately 0.28% of the female students have scores below 302.
It's important to note that the value mentioned, "97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits
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() Which number is closest to √5?
1.7
2.2
3.4
3.1
Answers
Answer:
Step-by-step explanation:
Each volleyball set costs $63.74.
Which equation represents the cost, c, of n sets?
Answers
The equation that represents the cost, c, of n sets is c = 63.74n
Which equation represents the cost, c, of n sets?from the question, we have the following parameters that can be used in our computation:
Each volleyball set costs $63.74.
Let the total number of sets be n
So we have
Cost of n = 63.74 * n
This gives
c = 63.74n
Hence, the equation is c = 63.74n
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If a firm’s total fixed costs are $11,639, total revenues are $28,200, and profit is $4,776, what must the firm’s total variable cost be?
Answers
Answer:
Step-by-step explanation:
What is the slope of the line that passes through the points (-2, 2), and (-4, -2)?
-1/2
2
-2
1/2
Answers
Answer:
The slope would be 2
Step-by-step explanation:
Please brainliest!
And hope this helped you!
I also answered first!
And tell me If I am wrong! :D
please help 6th grade math im new to it pleaae explain good
Answers
Answer:
0.6
Step-by-step explanation:
Given the trapezoid formula:
1/2(b1+b2/2)xH
We are given the numbers for the trapezoid:
0.3,0.9,1
To solve this here is what we are going to do.
1/2(0.9+0.3)x1
So add 0.9+0.3=1.2
Then Divide 1.2/2=0.6
So multiply 0.6 x 1=0.6
0.6 is your answer
(a) An angle measures 114°. What is the measure of its supplement?
(b) An angle measures 25°. What is the measure of its complement?
Answers
Answer:
33 and 147
Step-by-step explanation:
it im wrong tell me i will redo it i dont see answer choices
Determine a series of transformations that would map Figure P onto Figure Q.
Answers
Answer:
rotation 90° CW about the origintranslation up 5 unitsStep-by-step explanation:
You want a transformation that maps figure P in the 3rd quadrant to figure Q in the second quadrant.
RotationThe figures have the same orientation (sequence of angles and side lengths), so reflection is not needed as part of the transformation.
The shorter mid-length side in Figure P has a slope of -1, and the corresponding side in Figure Q has a slope of +1. This can be the result of a 90° clockwise rotation about the origin.
Rotation 90° CW about the origin will map the right-angle corner from (-7, -7) to (-7, 7).
TranslationThe right-angle corner in Figure Q is at (-7, 12), so a translation upward after the rotation is required. The amount of that translation is 12-7 = 5 units.
Translation upward by 5 units will map the right angle corner from its rotated position at (-7, 7) to its position in Figure Q at (-7, 12).
The series of transformations could be ...
Rotation 90° CW about the originTranslation up by 5 units__
Additional comment
The required transformation can be accomplished in one step by rotation 90° CW about the point (2.5, 2.5).
If Figure P is rotated 90° CW about its right-angle corner, then translation up by 19 units will map it to Figure Q. That is, there are many combinations of rotation and translation that will do the job.
A boat is 1000 meters from the base of a cliff. If the angle of depression from the top of the cliff to the boat is 15 degrees, how tall is the cliff? Round your answer to the nearest tenth
Answers
9514 1404 393
Answer:
267.9 m
Step-by-step explanation:
The relevant trig relation is ...
Tan = Opposite/Adjacent
In this geometry, the angle of depression is the angle of interest. The "adjacent" side of the triangle is the distance to the boat. The "opposite" side is the height of the cliff.
tan(15°) = height/(1000 m)
height = (1000 m)tan(15°)
height ≈ 267.9 m
The cliff is about 267.9 meters tall.
what will come in the following series 20 25 23 28 26 31 29 34 _? answer is 31. please explain how?? urgent pls
Answers
The series of numbers is adding 5 and then subtracting 2
20+5=25
25-2=23
23+5=28
28-2=26
and so on. Do you understand?
For the following vectors, (a) find the dot product v•w ; (b) find the angle between v and w , (c) state whether the vectors are parallel, octagonal, or neither. V=-3i-4j, w=6i+8j
A- v•w
B-the angle between v and w is theta ^•?
C- the vectors v and w are?
Answers
B) The angle between vectors v and w can be found using the formula: cos(theta) = (v • w) / (||v|| ||w||), where ||v|| and ||w|| are the magnitudes of vectors v and w respectively.
First, we need to find ||v|| and ||w||:
||v|| = sqrt((-3)^2 + (-4)^2) = 5
||w|| = sqrt((6)^2 + (8)^2) = 10
Now, we can substitute in the values to get:
cos(theta) = (-50) / (5 * 10) = -1
theta = arccos(-1) = pi radians or 180 degrees.
Therefore, the angle between vectors v and w is 180 degrees.
C) Two vectors are parallel if their directions are the same, which can be determined by comparing their unit vectors.
The unit vector of v is:
v_hat = v / ||v|| = (-3/5)i + (-4/5)j
The unit vector of w is:
w_hat = w / ||w|| = (6/10)i + (8/10)j = (3/5)i + (4/5)j
We can see that the unit vectors are in opposite directions, which means that the vectors are anti-parallel or opposite. Therefore, the vectors v and w are neither parallel nor orthogonal.
Need help with question #4
Answers
Question:
If n=8 and p=0.8, find P(r=7)
Answer:
0.33554
f(x) = 2x2 + 1, what is f(x) when x = 3?
Answers
Answer:
f(3) = 19
Step-by-step explanation:
Substitute 3 for x.
f(3) = 2(3)² + 1
f(3) = 2(9) + 1
f(3) = 18 + 1
f(3) = 19
What is 184739*23456
Answers
Answer:
that would be 4,333,237,984
Step-by-step explanation:
Answer:
4333237984
Step-by-step explanation:
184739*23456
Consider the following system of equations given in slope-intercept form. y = −1 3 x + 17, y = 5x - 23
Answers
The solution to the given system of equations is (7.5, 14.5). That is, x = 7.5, y = 14.5
Solving system of equationsFrom the question, we are to solve the given system of equations
The given system of equations is
y = −1/3x + 17
y = 5x - 23
Set the equations equal
That is,
−1/3x + 17 = 5x - 23
Now, solve for x
−1/3x + 17 = 5x - 23
Multiply through by 3
-1x + 51 = 15x - 69
51 + 69 = 15x + 1x
120 = 16x
Therefore,
16x = 120
x = 120/16
x = 7.5
Substitute the value of x into the second equation
y = 5x - 23
y = 5(7.5) - 23
y = 37.5 - 23
y = 14.5
Hence, the solution is (7.5, 14.5)
Here is the complete and correct question here:
Consider the system of equations given in slope-intercept form. y = −1/3x + 17, y = 5x - 23 The solution seems to be about (8, 14). Use the graphing calculator to find the exact values for the intersection point. What is the solution to this system of equations?
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What is the length of line segment AC?
Answers
Using geometry, we can find that the length of the line segment AC as per the distance between two points is= 18 ft.
What are line segments?
In geometry, a line segment's borders are determined by two distinct points on the line. Any portion of a line that connects two places is referred to as a line segment.
A segment has an endpoint, whereas a line doesn't.
What are some examples of line segments in the real world?
a scale, a ruler, a stick, and a boundary line.
Thus, the length of the line segment AC is = 18ft.
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An inner city revitalization zone is a rectangle that is twice as long as it is wide. The width of the region is growing at a rate of 34 m per year at a time when the region is 450 m wide. How fast is the area changing at that point in time?
Answers
Answer:
The area is changing at the point of \(\mathbf{61200 m^2/year}\)
Step-by-step explanation:
From the given information:
Let's recall from our previous knowledge that the formula for finding the area of a rectangle = L × w
where;
L = length and w = width of the rectangle
Suppose the Length L is twice the width w
Then L = 2w --- (1)
From The area of a rectangle
A = L × w
A = 2w × w
A = 2w²
Taking the above differentiating with respect to time
\(\dfrac{dA}{dt }= 4w \times \dfrac{dw}{dt} --- (2)\)
At the time t
\(\dfrac{dw}{dt}= 34 m \ per \ year ; w = 450 \ m\)
Replacing the values back into equation 2, we get:
\(\dfrac{dA}{dt }= 4 \times 450 \times 34\)
\(\mathbf{\dfrac{dA}{dt }= 61200 m^2/year}\)
Tracy drove 1.123 miles to her new job location. What is the actual distance written in scientificnotation. Help me please
Answers
we have the following:
\(1123=1.123\cdot10^3\)ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
Answers
Answer:
g = -1/2..................