Answer:
We conclude that the effectiveness is less than the 85% claim the company is making.
Step-by-step explanation:
We are given that a manufacturer of a new medication on the market for Crohn's disease makes a claim that the medication is effective in 85% of people who have the disease.
One hundred seventy-five individuals with Crohn's disease are given the medication, and 135 of them note the medication was effective.
Let p = percentage of people who have the Crohn's disease.
So, Null Hypothesis, [tex]H_0[/tex] : p = 85% {means that the effectiveness is equal to the 85% claim the company is making}
Alternate Hypothesis, [tex]H_A[/tex] : p < 85% {means that the effectiveness is less than the 85% claim the company is making}
The test statistics that would be used here One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of individuals who note the medication was effective = [tex]\frac{135}{175}[/tex] = 0.77
n = sample of individuals with Crohn's disease taken = 175
So, test statistics = [tex]\frac{0.77-0.85}{\sqrt{\frac{0.77(1-0.77)}{175} } }[/tex]
= -2.515
The value of z test statistics is -2.515.
Now, at 0.05 significance level the z table gives critical value of -1.645 for left-tailed test.
Since our test statistic is less than the critical value of z as -2.515 < -1.645, 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 the effectiveness is less than the 85% claim the company is making.
The study's findings suggest that the medication is less effective than the manufacturer's claim of 85%.
Step-by-Step Calculation
1. Define the parameter
The parameter we are testing is the population proportion p of people with Crohn's disease for whom the medication is effective. The manufacturer's claim is that [tex]\( p = 0.85 \)[/tex].
2. State the hypotheses
- Null hypothesis [tex]\( H_0 \): \( p = 0.85 \)[/tex]
- Alternative hypothesis [tex]\( H_a \)[/tex] : [tex]\( p < 0.85 \)[/tex]
3. Check conditions for the test
We use a one-sample z-test for proportions. The conditions are:
- Random sample: Assume the sample is random.
- Large enough sample size: Both [tex]\( np \)[/tex] and [tex]\( n(1-p) \)[/tex] should be greater than 10.
Calculations:
- [tex]\( np = 175 \times 0.85 = 148.75 \)[/tex]
- [tex]\( n(1-p) = 175 \times 0.15 = 26.25 \)[/tex]
Both values are greater than 10, so the conditions are met.
4. Perform the calculations
Sample proportion [tex]\( \hat{p} \)[/tex]:
[tex]\[ \hat{p} = \frac{135}{175} = 0.7714 \][/tex]
Standard error (SE) of the sampling distribution:
[tex]\[ SE = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.85 \times 0.15}{175}} = \sqrt{\frac{0.1275}{175}} = \sqrt{0.000728571} \approx 0.027 \][/tex]
Test statistic (z):
[tex]\[ z = \frac{\hat{p} - p}{SE} = \frac{0.7714 - 0.85}{0.027} = \frac{-0.0786}{0.027} \approx -2.91 \][/tex]
5. Determine the p-value
Using the standard normal distribution, we find the p-value for [tex]\( z = -2.91 \).[/tex]
Looking up this value in a z-table or using a statistical calculator, the p-value for [tex]\( z = -2.91 \)[/tex] is approximately 0.0018.
6. Make a decision
Since the p-value (0.0018) is less than the significance level [tex]\( \alpha = 0.05 \)[/tex], we reject the null hypothesis.
There is statistical evidence at the 0.05 significance level to support the claim that the effectiveness of the medication is less than 85%.
Solve the inequality: −2x > −6 Question 3 options: x < −3 x > 3 x > −3 x < 3
Answer:
divide both sides of the inequality by -2 and flip the inequality sign the you get (x < 3)
To solve the inequality -2x > -6, divide both sides by -2, remembering to reverse the inequality sign, to obtain x < 3 as the solution.
To solve the inequality -2x > -6, we start by isolating the variable x. To do this, we divide both sides of the inequality by -2. It's important to remember that when we divide or multiply both sides of an inequality by a negative number, we must reverse the direction of the inequality sign. Thus, dividing by -2, the inequality becomes x < 6/2. Simplifying further, we find that x < 3.
Others parts of the referenced information discuss concepts like absolute values, z-scores, and transitivity of numbers but are not directly relevant to solving this inequality.
Hence, the correct answer to the inequality is x < 3.
Alex needs to report his bowling average for the school newspaper. Here are his scores from the last 20 games: 132, 141, 110, 96, 154, 135, 111, 139, 102, 135, 133, 127, 99, 124, 129, 201, 131, 128, 134, and 135. Part A: What are the mean and median of this data? Part B: Which one of those two measures of central tendencies should he use for the newspaper and why? Part C: Are there any outliers? Please answer ASAP
Answer:
Part A:
Mean: 129.8
Median: 131.5
Step-by-step explanation:
The mean is the average so we add everything together and then divide it by however many numbers there are. 132 + 141 + 110 + 96 + 154 + 135 + 111 + 139 + 102 + 135 + 133 + 127 + 99 + 124 + 129 + 201 + 131 + 128 + 134 + 135 = 129.8
The median is the number in the middle. That is the number in between the rest from smallest to largest. 96, 99, 102, 110, 111, 124, 127, 128, 129, 131, 132, 133, 134, 135, 135, 135, 139, 141, 154, and 201
The medians are 131 and 132 so we add them together then divide by 2. That gives is 131.5 so that is our answer. I hope this helps and please mark me brainliest!
Help with mathematics
Answer:
ok
Step-by-step explanation:
Find the probability. Enter your answer as a simplified fraction.
Picking a purple marble from a jar with 15 green and 15 purple marbles.
The probability of picking a purple marble is
Answer:[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given
Jar contains 15 Green and
15 Purple marbles
Total marble[tex]=15+15=30[/tex]
Probability of Picking a Purple marble is
[tex]P=\frac{\text{No of Purple marble}}{\text{Total no of marble}}[/tex]
[tex]P=\frac{15}{30}[/tex]
[tex]P=\frac{1}{2}=0.5[/tex]
Therefore probability of picking a marble is [tex]0.5[/tex]
A plumber charges $130 2 hours of work and $235 for 5 hours of workWhat is the of change in dollars per hour
Final answer:
The plumber charges $35 per hour, calculated by dividing the change in total cost ($105) by the change in hours (3).
Explanation:
To find the rate of change in dollars per hour for the plumber's charges, we need to use the definition of rate of change, which is the change in cost divided by the change in time.
Here are the steps for calculation:
Determine the change in cost: $235 - $130 = $105.Determine the change in time: 5 hours - 2 hours = 3 hours.Calculate the rate of change: $105 ÷ 3 hours = $35 per hour.This means the plumber charges $35 per hour for their service.
The number of mosquitoes in Minneapolis, Minnesota (in millions of mosquitoes) as a function of rainfall (in
centimeters) is modeled by:
m(x) = -(x - 5)2 + 25
How many centimeters of rainfall will produce the maximum number of mosquitoes?
Answer:
5 cm
Step-by-step explanation:
Given the function:
[tex]m(x)=-(x-5)^{2} +25[/tex]
As we know the above function is a quadratic equation (vertical parabola) open downward and the vertex is the maximum number of mosquitoes.
The vertex form of a quadratic function is:
[tex]y=a(x-h)^{2} +k[/tex] where (h,k) is the vertex
Our given function have the vertex form as well, so the
(h,k) = (5,25)
At the height of 5 cm the rainfall will produce the maximum number of mosquitoes
Final answer:
In the function modeling the number of mosquitoes by rainfall, 5 centimeters of rainfall will produce the maximum number of mosquitoes, corresponding to the vertex of the parabola.
Explanation:
To find the number of centimeters of rainfall that will produce the maximum number of mosquitoes in Minneapolis, Minnesota, we look at the vertex of the parabolic function m(x) = -(x - 5)2 + 25. The vertex form of a parabola is given by f(x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola. In this equation, h represents the x-value that results in the maximum y-value for the parabola when a is negative, which corresponds to the maximum number of mosquitoes.
In this case, the vertex of the parabola is (5, 25), which tells us that 5 centimeters of rainfall will produce the maximum number, which is 25 million mosquitoes. This value is represented by h in the vertex form of the equation, indicating that the parabola opens downwards (since the coefficient of the (x - h)2 term is negative) and reaches its maximum at x = 5.
HELP!
What is the volume of the prism?
5.6 cm
4 cm
9 cm
7.8 cm
Answer:
Your answer
Step-by-step explanation:
Answer:140.4 is your answer!
Step-by-step explanation:hope this helped you!have an amazing rest of your night,afternoon or day!
Write in if/Then form: A shape has 4 congruent sides, if it is a rhombus.
Answer: If a shape has 4 congruent sides, then it is a rhombus.
Step-by-step explanation: I just added the words in the appropriate places.
can anyone help me with this question?
Answer:
I Believe its A
Step-by-step explanation:
IM so sorry if its wrong!!!!
but im pretty sure its right
Help?!!?? I don’t get it??
Answer:
1/6
Step-by-step explanation:
1/2 (The probability that its tails) x 1/3(The probability that it lands on a green side)
BRAINLIEST !!!!!!for whoever gives me explanation and answer
Answer:
100 x 0.85 = 85
100 x 0.85 = 85
85 x 2 = 170
170/85=2 so divide 100 by 2 = 50
50 x 0.85 = 42.5
50 x 0.85 = 42.5
42.5 + 42.5 = 85
Your answer is 500 hope this helps.
Step-by-step explanation:
At a carnival, you spin a spinner that has four equal-sized sections, each a different color: green, yellow, red, and blue. If you land on green, you win 2 points. If you land on yellow, red, or blue, you lose 1 point. Write the expected value equation. E (V) = StartFraction 1 Over a EndFraction (2) + StartFraction 1 Over b EndFraction (c) + StartFraction 1 OVer d EndFraction (e) + StartFraction 1 Over f EndFraction (g) a = b = c = d = e = f = g =
Answer:
a = 4
b = 4
c = -1
d = 4
e = -1
f = 4
g = -1
Step-by-step explanation:
To get the expected value equation you have to multiplicate the probability of each outcome by its reward and add them. The probability to get each color is 1/4 because the spinner has four equal-sized sections. If you win money, your reward is positive, but if you lost it, your reward is negative. Then:
expected value equation. E (V) = (1/4)*2 + (1/4)*(-1) + (1/4)*(-1) + (1/4)*(-1) = -0.25
Answer:
A 4
B 4
C -1
D 4
E -1
F 4
G -1
-0.25 points
lose 250 points
Solve the equation using the distributive property and properties of equality.
5(a+ 3) = -55
Answer:
a = -14
Step-by-step explanation:
Isolate the variable, a. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, divide 5 from both sides:
(5(a + 3))/5 = = (-55)/5
a + 3 = -55/5
a + 3 = -11
Next, fully isolate a by subtracting 3 from both sides:
a + 3 (-3) = -11 (-3)
a = -11 - 3
a = -14
a = -14 is your answer.
~
Final Answer:
a = -14In-depth explanation:
Hi! The question is asking us to solve the equation, which is:
[tex]\large\textbf{5(a + 3) = -55}[/tex]
Use the distributive property to simplify the left-hand side:
[tex]\large\textbf{5a + 15 = -55}[/tex]
Subtract 15 from each side:
[tex]\large\textbf{5a = -55 - 15}[/tex]
[tex]\large\textbf{5a = -70}[/tex]
Divide each side by 5:
[tex]\large\textbf{a = -14}[/tex]
∴ the answer is a = -14.[tex]\rule{350}{1}[/tex]
Describe the transformation f(x) = √x + 1 − 5 in words. The parent function f(x) = √x has been shifted 1 unit and 5 units.
We conclude that the parent function f(x) = √x has been shifted 1 unit to the left and 5 units downwards.
How was the parent function transformed?
For a function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N
If N is positive, the translation is upwards.If N is negative, the translation is downwards.For a function f(x), a horizontal translation of N units is written as:
g(x) = f(x) + N
If N is positive, the translation is to the left.If N is negative, the translation is to the right.Here we have f(x) = √x, and g(x) = √(x + 1) - 5
Then:
g(x) = f(x + 1) - 5
From this, we conclude that the parent function f(x) = √x has been shifted 1 unit to the left and 5 units downwards.
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Please help! in geo!
Answer:
pretty sure it would be 11 inches
Step-by-step explanation:
the rules of isosceles triangles is that two sides are the same and one is smaller.
Answer:
the missing side is 11 inches
Step-by-step explanation:
the missing angel is 37*
Is (1, 7) a solution to this system of inequalities? y < x + 8 y ≤ 6x + 1
Answer:
-8
Step-by-step explanation:
Final answer:
Upon checking both inequalities, the point (1, 7) satisfies y < x + 8 and y ≤ 6x + 1. Thus, (1, 7) is a solution to the system of inequalities.
Explanation:
To determine if the point (1, 7) is a solution to the given system of inequalities, we need to check if the point satisfies both inequalities. The system is:
y < x + 8
y ≤ 6x + 1
For the first inequality:
y < x + 8
7 < 1 + 8
7 < 9 ⇒ True
For the second inequality:
y ≤ 6x + 1
7 ≤ 6(1) + 1
7 ≤ 7 ⇒ True
Since the point (1, 7) satisfies both inequalities, it is indeed a solution to the system.
Will mark brainliest. Include explanation.
Answer:
D. 4x + 32; E. 4(x + 8)
Step-by-step explanation:
The correct answer is none. This problem is incorrect. The perimeter of a polygon is the sum of the lengths of all the sides. A perimeter is a length, not an area. A perimeter is expressed in feet, not square feet.
Ignoring the "square feet" part, once again, the perimeter is the sum of the lengths of all sides. Since this is a square, all sides have the same length, and there are 4 sides.
perimeter = 4s
perimeter = 4(x + 8) = 4x + 32
You want to estimate the number of eighth-grade students in your school who find it relaxing to listen to music. You consider two samples. Which sample is unbiased?
fifteen randomly selected members of the band
every fifth student whose name appears on an alphabetical list of eighth-grade students
Question 2
Explain.
You want to estimate the number of twelfth-grade students in a high school who ride a bus to school. Which sample is unbiased?
A. 4 students in the hallway
B. all students on the soccer team
C. 50 twelfth-grade students at random
D. 100 students at random during lunch
explain
A coin and a die is rolled. What is the probability of a head and a 3?
a. 1/4
b. 1/8
c. 1/12
d. 1/24
The sum of a number and 14 is at least 18
The inequality fir the given phrase is x+14≥18, the solution for the obtained inequality is x≥4.
The given phrase is "The sum of a number and 14 is at least 18".
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Let the unknown number be x.
Here, the inequality is x+14≥18
Subtract 14 on both the sides of an inequality, we get
x+14-14≥18-14
x≥4
Therefore, the inequality fir the given phrase is x+14≥18, the solution for the obtained inequality is x≥4.
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Final answer:
The sum of a number and 14 is at least 18' can be expressed as the inequality x + 14 >= 18, indicating that the unknown number must be 4 or greater.
Explanation:
The student's question involves setting up an inequality to represent the situation described.
The problem statement, 'The sum of a number and 14 is at least 18,' translates to a mathematical inequality as follows:
Let 'x' represent the unknown number.
The problem states that when you add 14 to this number, the result should be at least 18. Therefore, the inequality would be:
x + 14 >= 18.
To solve this inequality, you would subtract 14 from both sides:
x = 18 - 14
x = 4
This means the unknown number must be 4 or any larger number. In other words, any number greater than or equal to 4, when added to 14, will be at least 18.
Will give brainliest.
A candy company is designing the packaging for its new candy bar. the bars will be packed in cartons which are 1 foot long, 1 foot wide, and 1 foot high. how many of these cartons can they pack into the shipping crate which is 5 feet long, 12 feet wide, and 4 feet high?
Answer:
240 cartons
Step-by-step explanation:
First, I need to find the volume of the 2 objects.
If the measurements of the carton is 1 x 1 x 1, ultimately the volume of the carton is 1 cubic foot.
Then, to find the shipping crate volume, multiply 5 x 12 x 4. You will get 240 cubic feet.
Then, we need to find how many cartons can fit in the shipping crate. Divide 240 by 1, and obviously you get 240.
So, 240 cartons can be packed into the shipping crate.
Can you help me with this question?
Answer: the first one
Step-by-step explanation: can i have brainlieist
In January, Ben was charging $25 for individual hitting
lessons and in April started charging $30. What percent
did he increase his prices? _ _%
20% percentage increase in prices from $25 to $30.
To calculate the percentage increase:
Calculate the increase in price: $30 - $25 = $5
Calculate the percent increase: ($5 / $25) x 100% = 20%
Therefore, Ben increased his prices by 20%.
Could somebody help me with this please?
Answer:
Take a look below;
Step-by-step explanation:
See attachment;
BRAINLIEST URGENTTT
Jackie's gross semimonthly pay is $3420.
To maintain her current way of life, how much should she have saved by the time she retires?
$812,600
$820,800
$889,200
$890,600
Answer:
$890,600
Step-by-step explanation:
Answer:
They say you should save 10%
So if you calculate her yearly income
3420 x 26 pay periods per year = 88,920
Multiply it by 10
$889,200
Step-by-step explanation:
The graph represents this system of equations. A system of equations. y equals 4. y equals 3 minus StartFraction on-half EndFraction x. A coordinate grid with 2 lines. The first line passes through (negative 2, 4) and (0, 3). The second line passes through (negative 2, 4) and (0, 4). What is the solution to the system of equations? (–2, 4) (3, 4) (4, –2) (4, 3)
Answer:
b
Step-by-step explanation:
A coordinate grid with 2 lines. The first line passes through (negative 4, negative 3), (0, negative 3), and (4, negative 3). The second line passes through (0, negative 5) and (2, 4). The lines appear to intersect at about one-half, negative 3.
Solve the system of equations algebraically. Verify your answer using the graph.
y = 4x – 5
y = –3
What is the solution to the system of equations?
((StartFraction one-fourth EndFraction, negative 3), –3)
((StartFraction one-half EndFraction, negative 3), –3)
(–3, (negative 3, StartFraction 2 over 3 EndFraction))
The solution to the system of equations is (-2, 4).
The correct option is A.
We have,
y= 4
and, y= 3 - 1/2 x
To find the solution of Equation put y= 4 in equation 2 we get
4 = 3 - 1/2 x
4 - 3 = -1/2 x
1 = -1/2 x
x = -2
Thus, (-2, 4) is solution of Equation.
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Which of the following properties can numbers have?
They can be positive.
They can be zero.
They can be negative.
They can be both positive and negative.
They can be absolute value.
Answer:
They can be positive.
They can be zero.
They can be negative.
They can be absolute value.
Step-by-step explanation:
A number is an abstract entity used to describe quantity.
Zero, one, -1, 2.5, pi are all numbers.
The number is a member of one of the several classes: natural numbers, integers, rational numbers, real numbers, complex numbers, quaternions.
A number can't be both negative and positive.
The options 1, 2, 3, and 5 are correct.
What are numbers?A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them.
As per the given data:
We are given some properties of numbers in the options, and we have to find which among the following options are true.
They can be positive.
This is correct, as numbers can be positive
They can be zero.
This is correct, as a number can be zero.
They can be negative.
This is correct, as numbers can be negative.
They can be both positive and negative.
This is incorrect, as numbers can't be both positive and negative.
They can be absolute value.
This is correct, as numbers can have an absolute value.
Hence, the options 1, 2, 3, and 5 are correct.
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Henry can lay a brick walkway by himself in 12 hours. Roberts does the same job in 10 hours. Working together, how long will it take them to lay the brick walkway?
Please I need the answer right away!
Answer:
Henry = 12 hours
Robert = 10 hours
that 2 people
so 12/ divided by how many people
and 10/ divided by how many people
so 12/2
and 10/2
= 5 and 6
then find the (median) middle of both numbers one or more
which is 5 1/2
so they can finish working together in 5 1/2 hours
n Pensacola, Florida, the average rainfall in the month of July is $7.40$ inches. By October, the average rainfall decreases by $35\%$ . By December, the average rainfall drops another $0.66$ inches.
Answer:
Olani???
Why are you here?
(East harlem scholars academy teacher)
Step-by-step explanation:
The average rainfall in December is 4.15 inches. Therefore option C is the answer.
Given that, in Pensacola, Florida, the average rainfall in the month of July is 7.40 inches. By October, the average rainfall decreases by 35%. By December, the average rainfall drops another 0.66 inches.
We need to find the average rainfall, in inches, in December.
What is average rainfall?The term "average annual rainfall" refers to the sum of the yearly precipitation totals for a location during a year as determined by the nearest National Weather Service station over the three decades prior.
In July, rainfall was 7.40 inches. By October, the average rainfall decreases by 35%.
That is, 7.40-35% of 7.40
=7.40-0.35 × 7.40
=7.40-2.59=4.81
By December, the average rainfall drops another 0.66 inches.
That is, 4.81-0.66=4.15
The average rainfall in December is 4.15 inches. Therefore option C is the answer.
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Your question is incomplete, probably the complete question/missing part is:
In Pensacola, Florida, the average rainfall
in the month of July is 7.40 inches. By
October, the average rainfall decreases by
35%. By December, the average rainfall
drops another 0.66 inches.
What is the average rainfall, in inches, in
December?
A. 1.64
B. 1.93
C. 4.15
D. 4.81
The probability of a chance event is 0.05, it is
to happen
when compared to a chance event with a probability of 0.
Select one:
more likely
both more and less likely
less likely
equally likely
Answer:
less
Step-by-step explanation: