The value of x from the exponential equation is 2.866.
Logarithm:
A logarithm is a power to which a number must be raised to get some other number.
Here we have to find the value of x.
The equation is given:
[tex]6^{x}[/tex] = 170
Taking logarithms on both sides, we have:
log [tex]6^{x}[/tex] = log 170
x log 6 = log 170
x = log 170 / log 6
= 2.230/ 0.778
= 2.866
Therefore the value of x is 2.866.
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If one of the 255 subjects is randomly selected, find the probability that the person is over 40 given that he or she is a root beer drinker.
The probability that the person is over 40 given that he or she is a root beer drinker is 62.75%
The fact that
The ratio of the event space's size to the sample space's size represents an event's probability.
The total number of outcomes equals the size of the sample space.
The number of outcomes in the event you are interested in is the event space.
so
P = event space size divided by sample space size
step 1
determine the likelihood that the person is over 40 years old.
The sample size is 255.
event space size = 85
P=85/255------> P=1/3
step 2
determine the likelihood that they consume root beer.
The sample size is 255.
event space size = 75
P=75/255------> P=5/17
step 3
determine the likelihood that the individual is over 40 years old or that
They consume root beer.
so
P=(1/3)+(5/17)——-> P=(17*1+3*5)/51------> P=32/51-----> 0.6275——> 62.75%
therefore, the response is
32/51 or 62.75%
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Work out the values of A and B in these equivalent ratios.
A: 8:5
9:24: B
Answer:
A=3
B=15
Step-by-step explanation:
Since these are equivalent ratios, there is a constant scale factor for each number. As shown in the 8 and 24, we find the scale factor to be 24/8=3. This means that the second ratio's numbers are 3x bigger than the corresponding ones in the first ratio. A = 9/3 = 3, and B = 5*3=15
Match each word or phrase with the definition hypothesis null alternative Drag each word into the appropriate place below in order to correctly complete each of the following sentences. A _____ is a statement regarding a characteristic of one or more populations. The _____ ______ is a statement of no change, no effect, or no difference. The _____ ______ is a statement we are trying to find evidence to support. Drag your answer(s) to the correct position
A hypothesis is a statement regarding a characteristic of one or more populations. The null hypothesis is a statement of no change, no effect, or no difference. The alternative hypothesis is a statement we are trying to find evidence to support.
Generally, the null hypothesis expresses that there is no change, no difference, no effect, and in another way, no relationship between the independent and dependent variables. Because we are hypothesizing that nothing is happening, then it is called the null hypothesis.
The null and alternative hypothesis are two conflicting claims which researchers weigh evidence for and against using a statistical test. Null hypothesis (H0) means there is no effect in the population. Meanwhile, alternative hypothesis (Ha or H1) means there is an effect in the population.
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. SOSSSS I RESLLY NEED HELP WILL GIVE BRAINL
Answer:
If a polygon is not a triangle, then the polygon has more than three sides. Since a triangle has exactly 3 sides, contrapositive is true
Directions - Use the compound interest formula to calculate the final balance.
*
Formula: P (1+7
Compound Interest Formula: P
$300 compounded quarterly at 5% for 8 years.
Final balance = $
(if necessary, round to two decimal places)
The final balance is $446.44
What is compound interest ?
Compound interest is when you add the interest you've already earned back into your principal balance, which increases your returns by compounding them. Consider that you have $1,000 in a savings account with a 5% annual interest rate. You would make $50 in the first year, giving you a new balance of $1,050.
Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
r = 5/100
r = 0.05 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 300.00(1 + 0.05/4)^(4)(8)
A = 300.00(1 + 0.0125)^(32)
A = 446.44
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what kind of error is being made if the researcher fails to reject the null hypothesis when it is, in fact, false?
Rejecting a null hypothesis that is actually true in the population results in a type I error (false-positive); failing to reject a null hypothesis that is actually untrue in the Type II errors are produced by the population (false-negative).
Given that,
We have to find what kind of error is committed if the researcher doesn't rule out the null hypothesis even though it's incorrect.
We know that,
What is null hypothesis?To determine whether the provided experimental results are valid, the null hypothesis is a type of hypothesis that explains the population parameter. Depending on the viability of the given population or sample, this hypothesis is either rejected or not.
Rejecting a null hypothesis that is actually true in the population results in a type I error (false-positive); failing to reject a null hypothesis that is actually untrue in the Type II errors are produced by the population (false-negative).
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What does 0 on the x-axis mean?.
Answer:
Its the Origin
Step-by-step explanation:
Its ZERO
1. robin works as a server in a small restaurant, where she can earn a tip (extra money) from each customer she serves. the histogram below shows the distribution of her 60 tip amounts for one day of work.
The histogram below shows the distribution of her 60 tip amounts for one day of work.
a) The tips distribution is severely skewed to the right and unimodal. There is a large spread and high variability with a range of $22.50.b) The median is the average of the 30 th and 31st values, and a change in data value from $8 to $18 will not move the middle number.How to interpret Histogram?a) The distribution of tips is skewed right, whith a gap betwen 15 to 20 and a posible out lier at or above 20. The mean will be larger than the median, and the median will be in the $2,5 to $5 bar. Most tips are $5 or less, but there is some high variability with a range of $22.50.
b) The mean would increase because $18 is farther from the mean than $8. Also, more skew is added to the grapht $18 may be an out lier. This results in a larger mean.
The median: Should not change very much. The median is the average of the 30 th and 31st values, and a change in data value from $8 to $18 will not move the middle number.
Your question is incomplete, but most probably the complete question can be seen in the attachment.
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g in 2022, the maximum credit for child and dependent care expenses is $2,100 if only one spouse is employed and the other spouse is a full-time student.
The Child and Dependent Care Credit is a tax credit that helps parents and families pay for the care of their children and other dependents while they work, are looking for work, or are going to school.
Childcare and nursing care costs money! Luckily, there are tax deductions to cover the costs. If you had to pay someone to care for your children, family members, or spouse, find a job, go to school, or because of a disability, Child and Dependent Care credits are available.
You are generally eligible for the Child and Caregiver Tax Credit if you meet all of the following conditions:
Wages from work. If you are married and are filing a joint tax return, your spouse must also have income.Your application status is Single, Married and Co-Applicant, Head of Household, or Eligible Widow with her one dependent child.You (and your spouse in the case of a joint application) have income from employment or self-employment. You are exempt from this obligation if you were a full-time student or severely disabled.You paid someone to provide care for a beneficiary, but the provider is a dependent, beneficiary's parent, spouse, or child under the age of 19 (whether or not you are a dependent). It was not a person who could claim as a person.If you (and your spouse, if you are married) work, seek employment, attend school, or are disabled, you must pay for child care and maintenance.For year 2022, the Child and Caregiver Tax Credit is non-refundable. For eligible employment-related expenses, taxpayers can claim up to $3,000 for each eligible individual or one child, and up to $6,000 for two or more eligible individuals or children.
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What is a doubles plus one fact for 7 7?.
The doubles plus one fact for 7 7 is 7+7+1=15.
In layman's terms, Double Plus One Fact is a strategy for adding two consecutive numbers (numbers that are next to each other). To get the final result, simply add a smaller number to itself or double it and add 1.
Doubles fact are the numbers which are added with itself. such as 5+5=10, 3+3=6
so the doubles plus one fact are nothing but adding 1 to the result of doubles fact.
for given, doubles plus one fact for 7 7 is 7+7=14 and then adding 1 gives 14+1=15.
Hence, 7+7+1=15 is the doubles plus one fact for 7 7.
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Find the rectangular coordinates of the point whose spherical coordinates are given. (a) (3, 0, 0) (x, y, z) (b) (10, pi/3, pi/4)
the rectangular coordinates of the point whose spherical coordinates are given. (3, 0, 0) are (0.0.3)
What is spherical coordinates?
The coordinate system that is most frequently employed in three-dimensional systems is called spherical coordinates of the system, represented as (r,Ф,∅ ). The surface area in three dimensions is calculated using the spherical coordinate system. Radial distance, polar angles, and azimuthal angle are the three numbers that these coordinates indicate. Additionally known as spherical polar coordinates.
Given (r,Ф,∅ ) = (3,0,0)
x = rsin∅ cosФ = 3 * sin0 *cos0 = 0
y = rsin∅ sinФ = 3*0*0 = 0
z = rcos∅ = 3*1 = 3'
SO (x,y,y) = (0,0,3)
Hence the rectangular coordinates of the point whose spherical coordinates are given. (3, 0, 0) are (0.0.3)
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In what situation can you apply parallel lines cut by transversal?.
Some of the situations where we can apply parallel lines cut by transversal are mentioned below.
Transversal line is a line which cuts two or more coplanar lines. Coplanar lines are the lines which does not intersect each other.
The real life situations were we can apply parallel lines cut by transversal are:
Road and railway crossing.Railway tracks with sleepers.Wind screen wiper in cars.Window screens with multiple slats and the cord attached to them.Surface of a pineapple fruit.Badminton, tennis of volley ball nets.Thus, in real life there are many situations where parallel lines cut by transversal.
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What is the difference between research and practical research?.
Research or Basic research is purely thoretical in nature as its not easy to find its application in the real world. For example consider new theorems or Formula in mathematics, its difficult to find their practical use right away as it takes time to find the fields where they may be applicable.
Practical research is more focused on solving a known problem hence its use is already known or easy to find as it is derived from real world only.
Like Research in development of new medicine is practical in nature as we know for whic disease we are trying to cure from it.
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a food label states that a serving of a particular product contains 13 grams of total fat and 20 percent of the daily value. this means that
Using food labling :
The product contains 13 grams of total fat and 20 percent of the daily value. this means that
13 grams of fat provides 20% or one-fifth of the recommended total daily fat intake.
Food level :
food labels contain a lot of information about most packaged foods. Food labels are called "Nutrition Facts".itle or Job:
The US government requires food labels on most packaged foods. Labels provide complete, useful and accurate nutritional information. The government encourages food manufacturers to improve the quality of their products so that people can make healthier food choices.
Serving Sizes
Label serving sizes are based on the average amount of food people typically eat.
Label serving sizes are not necessarily healthy serving sizes.
Amount Per Serving
Total calories per serving are displayed in large print. This allows the consumer to count the number of calories per serving like total fat. Sodium; Total Carbs
PERCENT DAILY VALUE (% DAILY VALUE)
Many nutrients have a Percent Daily Value (%DV). This indicates how much each serving contributes to the total recommended daily intake of each nutrient. increase. This means that 13 grams of fat provides 20% or one-fifth of the recommended total daily fat intake.
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in the complement method, positive integers are represented as they would in in sign-and-magnitude format. the leftmost bit is still reserved as the sign bit. a negative integer is just the complement of the positive integer, with a 1 in the leftmost spot to represent the negative sign.
In the Binary method's complement method, positive integers are represented as they would in in sign-and-magnitude format. the leftmost bit is still reserved as the sign bit. a negative integer is just the complement of the positive integer, with a 1 in the leftmost spot to represent the negative sign
The method of complements is a technique to encode a symmetric range of positive and negative integers in a way that they can use the same algorithm for addition and subtraction throughout the whole range
Changing the sign of any number is encoded by generating its complement, which is usually done by a very simple and efficient algorithm
Therefore, In the Binary method's complement method, positive integers are represented as they would in in sign-and-magnitude format.
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Sophie wa building a fence around her flower bed. The width mut be twice the length to fit in her backyard. She only ha 72 feet of fencing. What i the maximum width he can build?
The length of the fencing is 12 feet and the width of the fencing is 24 feet.
What is length and width?
The dimensions of length and width are crucial in the study of geometry because they help define the models.
Given in the question,
The width must be twice the length,
So, Let the length as L and and the width will be equal to 2L.
Total fencing = 72 feet.
Assuming the flower bed to be rectangular.
The total perimeter = 2(Length + width)
72 = 2(L + 2L)
72 = 6L
L = 12,
So length will be 12 feet,
And, width will be 2L = 24 feet.
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Evan is single and has AGI of $277,300 in 2019. His potential itemized deductions before any limitations for the year total $52,300 and consist of the following:
Medical expenses (before the AGI limitation)$29,000
Interest on home mortgage 8,700
State income taxes 9,500
Real estate taxes 3,600
Charitable contributions 2,500
After all necessary adjustments are made, what is the amount of itemized deductions Evan may claim? If required, round the medical deduction to the nearest dollar and use the rounded amount in subsequent computations.
Evan's total itemized deduction is $
22,470
Evan's total itemized deduction is found as $24,400.
Define the term itemized deduction?The costs you incurred for state and local income as well as sales taxes, property investment taxes, personal state taxes, mortgage interest, including disaster losses are all included in itemised deductions. You can also count charitable donations and a portion of your out-of-pocket medical and dental costs.Only if medical expenses exceed 7.5% of your AGI may they be written off:
$277,300 x 7.5% = $20,797.50
Medical expenses: = $29,000 - $20,797.50
Medical expenses = $8,202.50.
Evan can write off $8,700 in interest on a mortgage.
$5,000 is the maximum deduction for state plus local taxes for just a single filer.
Contributions to charities are also tax deductible up to $2,500
Deductions totaled = $8,202.50 + $8,700 + $5,000 + $2,500
Deductions totaled = $24,402.50
Thus, Evan's total itemized deduction is found as $24,400.
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How do you know if its SAS or ASA?.
SAS: denotes the existence of two triangles whose two sides and included angle are known to be equal.
ASA: denotes the existence of two triangles whose included side and two known angles are equal.
Define the SAS or ASA congruenecies?SAS (side, angle, side):
Using the acronym SAS, which stands for "side, angle, side," we can denote the equality of the sides and angles of two triangles.The triangles are congruent if two sides and the associated angle of one triangle match the corresponding sides and angle from another triangle.Angle, Side, Angle, or ASA:
ASA, which stands for "angle, side, angle," denotes the existence of two triangles whose included side and two known angles are equal.The triangles are congruent if two angles and the enclosed side of one triangle match the corresponding angles and side from another triangle.To know more about the SAS or ASA congruenecies, here
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Select the correct answer.
Victor solved this inequality as shown:
Step 1: 3x − 5 > x + 5
Step 2: 2x − 5 > 5
Step 3: 2x > 10
Step 4: x > 5
What property justifies the work between step 3 and step 4?
A.
division property of inequality
B.
inverse property of multiplication
C.
subtraction property of inequality
D.
transitive property of inequality
The correct justification for moving from step 3 to step 4 in victor's solution is A. division property of inequality
What is division property of inequality?According to the division property of equality, if we divide an equation's two sides by the same number, the equation doesn't change.
Let's say you have two identically sized pizzas. You divide each one into halves and serve your buddies one half of each pizza. You will have equal pieces of both pizzas left over if you measure
as regards the Victor's problem division of both sides of the equation by 2 is achieved by the division property of inequality
Instance of division property of inequality dividing by 2
Step 3: 2x > 10
Step 4: x > 5
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switch the order of integration for the double integrals below from dy dx to dx dy, or vice versa. (hint: draw the region on the xy-plane to understand the order.) you are not required to evaluate/solve the double integral: just rewrite it. (a) z 2 0 z 3y 0 (x 4 y e 4yx) dx dy
The order of integration for the double integrals below from dy dx to dx dy, or vice versa is I = ₀∫⁴ √x∫y² eˣ/y² dydx
We need to switch the order of integration
I = ₀∫⁴ ₀∫ⁿ √(xy) dxdy
From n = 0 to n = 4
y = 0 to y = n
Taken horizontal strip
on strip values of y will be fixed and values of x will be varied.
Limits of y are
y = 0 to y = 4
limits of x are
x = y to x = 4
I = ₀∫⁴ ₀∫ⁿ √(xy) dxdy
I = ₀∫² ₀∫y² eˣ/y² dxdy
Taking vertical strip
on strip values of x will be fixed and values of x will be varied.
limits of x are
x = 0 to x = 4
Limits of y are
y = √x to y = 2
I = ₀∫⁴ √x∫y² eˣ/y² dydx
Therefore, the order of integration for the double integrals below from dy dx to dx dy, or vice versa is I = ₀∫⁴ √x∫y² eˣ/y² dydx
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What is the final step in solving the inequality 2/5 4x 6x 4 x 3 x 3x 3x 3?.
The final step in solving the given inequality is defining the range according to the final value of x as (-Inf,3).
In Variable based math, inequality is a numerical explanation that shows the connection between two articulations utilizing the imbalance image. The articulations on the two sides of a disparity sign are not equivalent. It implies that the articulation on the left-hand side ought to be more prominent than or not exactly the articulation on the right-hand side or the other way around.
On the off chance that the connection between two mathematical articulations is characterized utilizing the imbalance images, then it is called exacting disparities.
We have inequality as –2(5 – 4x) < 6x – 4
Step1: -10+8x<6x-4
Step2:8x-6x<-4+10
Step3:2x<6
Step4:x<3
Step5:Range of value of x as (-Inf,3)
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(Complete question) is:
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
9. a plane flies from base camp to lake a, 280 km away, in a direction of 200 north of east. after dropping off supplies it flies to lake b, which is 190 km at 30 0 west of north from lake a. graphically and check using trig, determine the distance and direction from lake b to camp.
The distance from lake b to camp is 310 km and the direction of lake b to camp is 57° S of W.
Distance is a numerical value. The length between the two points is measured by distance. The face or position of an object or person can be said by direction.
There are four cardinal directions which are the main four compass directions. The four directions are North, East, West and South. North-East, North-West, South-East and South-West also come under directions.
As per the question,
Distance from base camp to lake a = 280 kmThe direction of the plane = 20.0° north of east Distance to lake b = 190 kmThe direction of the plane = 30.0° west of northWith a scale of unit 1, the vector from the base camp to the lake to the vector connecting lakes a and b is graphically represented.
Therefore, 310 km is the distance from the lake b to base camp and 57.0° south of west is the direction of the plane.
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a) 3 cups cost £7 in total. How much do 15 cups cost?
b) 4 glasses cost £24 in total. How much do 7 glasses cost?
The cost of 15 cups is £35 and the cost of 7 glasses is £42 after applying the concept of the linear equation.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Let the cost of 15 cups is x
3 → 7
15 → x
3/15 = 7/x
1/5 = 7/x
x = £35
The cost of 7 glasses:
= (24x7)/4
= £42
Thus, the cost of 15 cups is £35 and the cost of 7 glasses is £42 after applying the concept of the linear equation.
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a survey on internet usage was conducted among a group of 200 students in the school cafeteria. it was found that 100 students spend at least two hours online every day. which of these is an example of descriptive statistics?
The example of descriptive statistics is d) 50% of the students surveyed spend at least two hours online each day.
Given:
a survey on internet usage was conducted among a group of 200 students in the school cafeteria. it was found that 100 students spend at least two hours online every day.
Here number of possible outcomes = 200
Number of favorable outcomes = 100
Probability p = 100/200
= 1/2
= 0.5
= 0.5*100%
= 50%
Therefore 50% of the students surveyed spend at least two hours online each day.
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Full question:
A survey on Internet usage was conducted among a group of 200 students in the school cafeteria. It was found that 100 students spend at least two hours online every day.Which of these is an example of descriptive statistics?a.) 50% of the students surveyed spend at least two hours online each day.b.) 50% of the students in the school spend at least two hours online each day.c.) 50% of the students in a class spend at least two hours online each day.d.) 50% of the students in the cafeteria spend at least two hours online each day.
What does M mean in parallel lines?.
m mean slope in parallel lines and it is always same in two parallel lines.
Given:
Linear equations are generally described by the slope-intercept
represented by the equation y = mx+b
where m = slope
b = y-intercept.
In parallel lines:
Slope is always same means that two parallel lines have same slopes because those are not intersect at any point.
Example:
y = 3x + 4
here slope m = 3
The parallel line to this equation is also have the same slope.
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Question
The function C(x)=17.5x−10 represents the cost (in dollars) of buying x tickets to the orchestra with a $10 coupon.
a. How much does it cost to buy 5 tickets?
It costs $
to buy 5 tickets.
b. How many tickets can you buy with $130?
You can buy
tickets.
Answer:
a. $77.5
b. 8 tickets
Step-by-step explanation:
a. Replacing x with 5 in the equation to get the cost of 5 tickets would look like this:
C(x = 5) = 17.5x - 10 = 17.5(5) - 10 = 87.5 - 10 = 77.5
b. There's no smart way to do this aside from picking a number of tickets that costs less that $130 and checking the total cost to buy another ticket until we go over $130
From a, we know that 5 tickets is $77.5
and every additional tickets costs $17.5
so 6 tickets is $77.5 + $17.5 = $95
so 7 tickets is $95 + $17.5 = $112.5
so 8 tickets is $112 + $17.5 = $130
How do you know if infinity is positive or negative on a graph?.
In general, the limit will reach infinity or negative infinity when you take a limit and the denominator is equal to zero (depending on the sign of the function).
The number zero is not a real number. It is a mathematical notion used to symbolize an extremely huge value that is theoretically impossible to obtain. Limit solutions imply that the equation you are getting the limit of will continue to go in that direction indefinitely. The graph approaches but never touches the y-axis (represented by x = 0) because you have a vertical asymptote there. g(x) = 1/(x2) will continue to rise as you approach x = 0 from the right or left. You can picture it continuing upwards after it leaves the page. In other words, because g(x) keeps increasing indefinitely as x approaches 0, its limit is infinity.
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Which fractions have a least common denominator of 20?
Answer:
Step-by-step explanation:
Two different fractions where lowest common denominator is 20 are 1/4 and 1/5.
What are the lowest common denominator?
For two or more fractions, if the numbers at the bottom (or denominator) by which the lowest number can be divide into, is called the lowest common denominator. It is also known as the least common denominator.
Here, 20 is the given lowest common denominator.
Therefore, we can write: 20 = 1 × 20, 20 = 2 × 10, 20 = 4×5
Hence, two fractions for which 20 can be a lowest common denominator are 1/4 and 1/5.
Hope it helps!
A highly risk-averse investor is considering adding one additional stock to a 3-stock portfolio, to form a 4-stock portfolio. The three stocks currently held all have b = 1.0, and they are perfectly positively correlated with the market. Potential new Stocks A and B both have expected returns of 15%, are in equilibrium, and are equally correlated with the market, with r = 0.75. However, Stock A's standard deviation of returns is 12% versus 8% for Stock B. Which stock should this investor add to his or her portfolio, or does the choice not matter?
Either A or B, i.e., the investor should be indifferent between the two.
Stock A.
Stock B.
Neither A nor B, as neither has a return sufficient to compensate for risk.
Add A, since its beta must be lower.
As per the standard deviation, The B stock portfolio is more risk-efficient in simple words.
Standard deviation:
Basically, standard deviation means the measure of how dispersed the data is in relation to the mean.
And the low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given,
A highly risk-averse investor is considering adding one additional stock to a 3-stock portfolio, to form a 4-stock portfolio. The three stocks currently held all have b = 1.0, and they are perfectly positively correlated with the market. Potential new Stocks A and B both have expected returns of 15%, are in equilibrium, and are equally correlated with the market, with r = 0.75. However, Stock A's standard deviation of returns is 12% versus 8% for Stock B.
Here we need to find in which stock should this investor add to his or her portfolio, or does the choice not matter.
Here we know that either of these shares would yield the same expected return for the entire portfolio if added to the same share of the portfolio.
So, if stock B is included in the portfolio, the expected standard deviation for the portfolio will be lower, since the standalone deviation is lower.
And therefore, lower risk or volatility, or standard deviation of the portfolio for the same level of the expected return on the new portfolio.
Therefore, the ratio of Sharpe to stock B will be higher. The B stock portfolio is more risk-efficient in simple words.
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In randomized, double-blind clinical trials of a new vaccine, children were randomly divided into two groups. Subjects in group 1 received the new vaccine while subjects in group 2 received a control vaccine. After the second dose, 136 of 450 subjects in the experimental group (group 1) experience drowsiness as a side effect. After the second dose, 39 of 95 of the subjects in the control (group 2) experienced drowsiness as a side effect. Does the evidence suggest that a different proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the a = 0.05 level of significance?
What is the result of this hypothesis test?
A. Reject the null hypothesis because there is sufficient evidence to conclude that the population proportions are different.
B. Accept the alternative hypothesis because there is sufficient evidence to conclude that the population proportions are different.
C. Do not reject the null hypothesis because there is not sufficient evidence to conclude that the population proportions are different.
According to the evidence, we cannot conclude that the lower proportions of drowsiness in group 1 subjects is the side effect of the subjects in group 2., at alpha equals 0.05 level of significance. Thus, the correct option is C.
It is given that in the double-blind clinical trial, children are divided into two groups.
[tex]H_0 : p1=p2\\[/tex]
[tex]H_a: p1 > p2[/tex]
Now, N1= 450 , P1=136/450=0.3022
N2=95, P2=39/95=0.410
We have to now state the null and alternative hypotheses and draw conclusions based on them.
Now, the test statistics are done as follows:
Z= [tex]p1-p2/\sqrt{p1*1-p1/n1+p2*1-p2/n2}[/tex]
Z= [tex]0.3022-0.410/\sqrt{0.3022*1-0.3022/450+0.410*1-0.410/95}[/tex]
Z= [tex]-0.10/\sqrt{4.686+0.0025}[/tex]
Z= -0.10/2.165
Z= -0.04
At the significance level of 0.05.
Decision: We will reject the null hypothesis if the value of Z is less than the critical value
Critical value at Z(0.05)= -1.645
Thus, we will not reject the null hypothesis as the value of z is greater than the critical value. Thus, in this situation, we cannot conclude that the lower proportions of drowsiness in group 1 subjects as the side effect of the subjects in group 2.
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