a. Yes, the distribution of the number of cases of type II diabetes in the United States can be approximated by a Poisson distribution since it is a rare event and the number of cases is independent of each other.
b. The probability is calculated as P(X ≤ 10) = e^(-12) * 12^10 / 10!, which is approximately 0.112.
c. we can subtract the probability of X ≤ 10 from the probability of X ≤ 15. The probability is calculated as P(10 < X < 15) = P(X ≤ 15) - P(X ≤ 10) = e^(-12) * (12^11 / 11! + 12^12 / 12! + 12^13 / 13! + 12^14 / 14!) ≈ 0.215.
d. The probability of observing 19 or more cases can be calculated using the Poisson distribution formula, P(X ≥ 19) = 1 - P(X ≤ 18) = 1 - e^(-12) * (12^0 / 0! + 12^1 / 1! + ... + 12^18 / 18!) ≈ 0.0002, which is a very small probability.
a. The distribution of the number of cases of type II diabetes in the United States can be approximated by a Poisson distribution if the cases are rare, random, and independent events. Given the incidence rate of 12 per 100,000, it can be considered a rare event, and if we assume the cases are independent and random, we can approximate the distribution using a Poisson distribution. The mean (λ) is equal to the incidence rate, which is 12 cases per 100,000.
b. To find the probability that the number of cases of type II diabetes is less than or equal to 10 per 100,000, we need to calculate the cumulative probability for the Poisson distribution with λ = 12 and k = 10. This can be found using the formula:
P(X ≤ 10) = Σ [e^(-λ) * (λ^k) / k!] for k = 0 to 10
c. To find the probability that the number of cases of type II diabetes is greater than 10 but less than 15 per 100,000, we need to calculate the probability for the Poisson distribution with λ = 12 and k = 11, 12, 13, and 14. This can be found using the formula:
P(10 < X < 15) = Σ [e^(-λ) * (λ^k) / k!] for k = 11 to 14
d. To determine if we would expect to observe 19 or more cases of type II diabetes per 100,000 in the United States, we can find the probability of observing 19 or more cases using the Poisson distribution with λ = 12. This can be found using the formula:
P(X ≥ 19) = 1 - P(X ≤ 18) = 1 - Σ [e^(-λ) * (λ^k) / k!] for k = 0 to 18
If the probability is low (typically less than 0.05), then it would be unlikely to observe 19 or more cases of type II diabetes per 100,000 in the United States.
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g in a simple undirected graph with 8 vertices and 27 edges, how many vertices can have degree 7?
In a simple undirected graph with 8 vertices and 27 edges, the maximum degree for a vertex is 7, since a vertex can connect to all other vertices. To determine the number of vertices that can have degree 7, we will consider the properties of simple graphs and the relationship between vertices, edges, and degrees.
In a simple graph, there are no self-loops or multiple edges between the same pair of vertices. Therefore, the maximum number of edges in a simple graph with n vertices can be calculated using the formula:
[tex]Max edges = n(n-1)/2\\[/tex]
For our graph with 8 vertices, the maximum number of edges is:
Max edges = 8(8-1)/2 = 8(7)/2 = 28
Since our graph has 27 edges, it is almost a complete graph (which would have 28 edges). To figure out how many vertices can have a degree of 7, we can examine the degrees of other vertices.
If we have one vertex with degree 7, the remaining 7 vertices will be fully connected to each other, forming a complete subgraph with 7 vertices. The number of edges in this subgraph is:
Edges = 7(7-1)/2 = 7(6)/2 = 21
The total number of edges in the graph, including the vertex with degree 7, is 21 + 7 = 28. Since our graph has 27 edges, we need to remove one edge from this configuration. We can remove one edge between two of the vertices that are not the vertex with degree 7. By doing this, we maintain the degree 7 for the first vertex while reducing the degrees of two other vertices to 6.
Therefore, in a simple undirected graph with 8 vertices and 27 edges, 1 vertex can have a degree of 7.
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1/3 times 3/5 please I don’t know help
(Chapter 12) For any vectors u and v in V3, (u + v) X v= (u X v)
After substitution, we get (u + v) X v = u X v + 0, which simplifies to (u + v) X v = u X v thus proving that (u + v) X v = u X v for any vectors u and v in V3.
To prove the statement (u + v) X v = u X v for any vectors u and v in V3, we will use the properties of the cross product. First, we know that the cross product is distributive over addition, meaning that (u + v) X v = u X v + v X v.
However, we also know that the cross product of a vector with itself is zero, since the angle between the two vectors is zero degrees. Therefore, v X v = 0.
Substituting this into the previous equation gives us (u + v) X v = u X v + 0, which simplifies to (u + v) X v = u X v.
Therefore, we have proven that (u + v) X v = u X v for any vectors u and v in V3.
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Find the area of the figure below formed from a triangle and a parallelogram
The area of the figure formed from a triangle and a parallelogram is 22 sq units
Finding the area of the figureFrom the question, we have the following parameters that can be used in our computation:
Figure formed from a triangle and a parallelogram
The area is
Area = Triangle + Parallelogram - Common area
Using the area formulas, we have
Area = 5 * 4 + 1/2 *8 * 3 - 1/2 * 4 * 5
Evaluate
Area = 22
HEnce. the area is 22 sq units
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Answer this question please!
a) There is no enough evidence of an increase in life expectancy.
b) P-value=0.07.
The P-value indicates that this sample result is not rare to happen (is greater than the significance level) even if the mean of the population is still 87 hours.
We have to perform a hypothesis test on the mean, with known standard deviation of the population.
The null hypothesis, which we will reject or not, states that the life expectancy has not increase (it stays equal or less than 87 hours).
The null and alternative hypothesis are
H₀: μ ≤ 87
H₁ : μ > 87
The significance level is α=0.01.
The z-value is
z = 1.5
The P-value for z is = 0.06681
The P-value (0.07) is greater than the significance level (0.01), so the effect is not significant. We fail to reject the null hypothesis.
There is no enough evidence of an increase in life expectancy.
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complete question:
D" size batteries produced by MNM Corporation have had a life expectancy of 87 hours. Because of an improved production process, the company believes that there has been an increase in the life expectancy of its "D" size batteries. A sample of 36 batteries showed an average life of 88.5 hours. Assume from past information that it is known that the standard deviation of the population is 9 hours.
(a) Use a 0.01 level of significance, and test to determine if there has been an increase in the life expectancy of the "D" size batteries.
(b) What is the p-value associated with the sample results? What is your conclusion, based on the p-value?
What is the volume of the prism?
Enter your answer, as a mixed number in simplest form, in the box.
cm³
pls hlp thx your the best
The total cost for 13 rides is 46 $.
Amount to be paid as entry fee = 20 $
Amount to be paid in each ride = 2 $
Therefore, total cost for 13 rides, P = 20 + (2 x 13)
P = 46 $
Total cost for r rides, P' = (20 + 2r) $
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13 describe a situation in which you believe it would be appropriate to perform a regression analysis in a social service agency with which you are familiar? how would the results13 describe a situation in which you believe it would be appropriate to perform a regression analysis in a social service agency with which you are familiar? how would the results help the agency? help the agency?
One situation in which a social service agency may want to perform a regression analysis is when they are trying to determine the factors that contribute to the success or failure of their programs.
For example, let's say the agency runs a job training program and they want to know which factors (such as age, education level, or prior work experience) are most strongly correlated with program completion and employment outcomes for participants.
Performing a regression analysis can help the agency identify these key factors and assess their relative importance. This information can then be used to make targeted improvements to the program, such as adjusting the curriculum or offering additional support services to address specific barriers to success.
Additionally, the results of the regression analysis can be used to make a stronger case for the effectiveness of the program to funders and stakeholders. By being able to demonstrate a clear link between program participation and positive outcomes, the agency may be more likely to receive continued support and funding for their services.
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question # 1
How many people were in the survey shown in the frequency table?
A. 42
B. 27
C. 30
D. 10
question # 2
What is wrong with the frequency table?
A. There is nothing wrong with the table.
B. The tallies are not totaled correctly.
C. There is not enough data.
D. There should be a row for 58.
question # 3
Which example would be likely to give a valid conclusion?
A. People leaving the library are asked if they like to read.
B. Five students are asked how tall they are.
C. The teacher displays the class's test scores in stem-and-leaf plot.
D. Eight tall people are measured to find the height of a 5th grade student.
question # 4
How many people were in the survey shown in the frequency table?
A. 34
B. 32
C. 13
D. 30
question # 5
What is wrong with the frequency table?
A. The tallies are not totaled correctly.
B. There should not be a row for 57.
C. There is nothing wrong with the table.
D. There is not enough data.
Answer:
Question 1: 27
Question 2: nothing wrong with the table
Question 3: Not sure which one to pick
Question 4: 15
Question 5: There is not enough data
Step-by-step explanation:
[tex]Question[/tex] #1
In the first picture we can see that if we add up all the frequencies we can conclude to: 2+15+8+2
= 27.
Thus the answer to question 1 is, 27
[tex]Question[/tex] #2
By looking at the FIRST picture what I can conclude is that there should be nothing wrong with the table. ( Not 100% sure )
Thus the answer to question 2 is, nothing wrong with the table
[tex]Question[/tex] #3
For this one I am not sure.
[tex]Question[/tex] #4
Well by looking at the SECOND picture I can conclude by adding:
1+8+4+2 = 15
Thus the answer to question 4 is, 15
[tex]Question[/tex] #5
Well looking at it judging by the picture given what I can conclude is that there is not enough data for the frequency.
Thus the answer to question 5 is, there is not enough data
Answer:
#1 A- 42
#2 D- Should be a row for 58
#3 A- Asking people leaving the library if they like to read
#4 C- 13
#5- Nothing wrong with the table
(b) -0.99 As in part (a), we are given a z test statistic and we will calculate the corresponding P-value. Here the value of the z test statistic is -0.99. We previously determined that since the alternative hypothesis is of the form p < Po, the P-value is the area under the z curve to the left of the calculated value of the test statistic. Using SALT, we find that the cumulative probability associated with a z test statistic of -0.99, rounded to four decimal places, is -1.6449 x The cumulative probability is exactly the area under the z curve to the left, so we can use the cumulative probability to find the P-value, rounding the answers to four decimal places. P-value = (z curve area to the left of -0.99) = ____
The P-value is 0.1611.
P-value = 0.1602
You are given a z-test statistic of -0.99, and you want to find the corresponding P-value. The P-value represents the probability of observing a test statistic as extreme as, or more extreme than, the one calculated, given that the null hypothesis is true.
Step 1: Identify the z-test statistic
The z-test statistic is given as -0.99.
Step 2: Find the cumulative probability associated with the z-test statistic
Using a z-table or a statistical software, you can find the cumulative probability associated with a z-test statistic of -0.99.
Step 3: Determine the P-value
The cumulative probability you find in Step 2 is equivalent to the P-value since the alternative hypothesis is of the form p < p₀, and the P-value is the area under the z curve to the left of the calculated value of the test statistic.
P-value = (z curve area to the left of -0.99)
After finding the cumulative probability in a z-table or using a statistical software for a z-score of -0.99, you get:
P-value = 0.1611 (rounded to four decimal places)
So, the P-value is 0.1611.
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If x is a nontrivial solution of Ax=0, then every entry in x is nonzero. T/F?
The statement "If x is a nontrivial solution of Ax=0, then every entry in x is nonzero" is False.
A nontrivial solution means that there is at least one nonzero entry in x. However, it doesn't imply that every entry in x must be nonzero. It's possible to have a mixture of nonzero and zero entries in a nontrivial solution.
If x is a nontrivial solution of Ax=0, it means that x is a nonzero vector in the null space of A. This implies that A x = 0, which means that the linear combination of the columns of A given by x results in the zero vector.
However, this does not necessarily mean that every entry in x is nonzero. For example, consider the matrix A given by:
A = [1 0 1;
0 1 1;
1 1 2]
The null space of A contains the vector x = [-1; 1; 1], which is a nontrivial solution of Ax = 0. However, this vector has one entry that is zero and two entries that are nonzero.
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HELP PLEASEEEEE!!! (LOOK AT THE PICTURE AND READ CAREFULLY).
Answer:
1 False
2 True
3 True
4 False
Mitchell went on a shopping trip to San Francisco. He purchased a new jacket originally priced at $98 but discounted 18%. How much did he pay for the computer? Round your answer to the nearest cent.
The actual amount of money that Mitchell bought the computer after the discount deductions would be = $80.36
How to calculate the discounted price of the computer?The original price of the computer = $98
The percentage discount = 18% of cost price.
That is ; 18/100 × 98/1
= 1764/100 = $17.64
Therefore the discounted price of the computer = original price - discount price = 98-17.64 = $80.36
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Question 1 Bicycles in the late 1800s looked very different than they do today. a. How many rotations does each tire make after traveling 600 feet? Round your answers to the nearest whole number.
The number of revolutions small wheel took is 127 and the number of revolutions large wheel took is 19.
Given that, the distance travelled 600 feet.
We know that, 1 feet = 12 inches
From the given figure,
Radius of larger wheel of bicycle is 60 inches
60 inches = 60/12 = 5 feet
Radius of larger wheel of bicycle is 9 inches
9 inches = 9/12 = 0.75 feet
We know that, circumference of a circle is 2πr.
Circumference of small wheel = 2×3.14×0.75
= 4.71 feet
Number of revolution = 600/4.71
= 127.38
≈ 127
Circumference of large wheel = 2×3.14×5
= 31.4 feet
Number of revolution = 600/31.4
= 19.1
≈ 19
Therefore, the number of revolutions small wheel took is 127 and the number of revolutions large wheel took is 19.
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37. Perform the following binary multiplications, assuming unsigned integers: b) 10011 x 1011
The binary multiplication of 10011 and 1011, assuming unsigned integers, is 1000101 (209 in decimal).
To perform the binary multiplication of 10011 (19 in decimal) and 1011 (11 in decimal), follow these steps:
1. Write down the two binary numbers, with the larger one on top:
10011
x 1011
2. Starting from the rightmost digit of the bottom number, multiply it by the entire top number, writing the product below, aligned with the current digit:
10011
x 1011
-----
10011 (1 * 10011)
3. Move one position to the left in the bottom number, and repeat step 2. Add a zero to the rightmost position of the product to account for the place value:
10011
x 1011
-----
10011
00000 (0 * 10011)
4. Continue this process for each digit in the bottom number:
10011
x 1011
-----
10011
00000
10011 (1 * 10011)
5. Finally, add all the products together:
10011
x 1011
-----
10011
00000
10011
-----
1000101 (final product)
So, the binary multiplication of 10011 and 1011, assuming unsigned integers, is 1000101 (209 in decimal).
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First grade level equation 5x+2x=-8-6
Answer:
x = -2
Step-by-step explanation:
5x + 2x = -8 - 6
7x = -14
x = -2
can someone help with question 19
Answer:
48. 192
Step-by-step explanation:
In order to get from 3/4 to 3/16, one way would be to divide by 4. Another way is to multiply 3/4 by 1/4.
You can test whether multiplying by 4 works by multiplying 3/4 by 4 and 3 by 4.
When 3/4 is multiplied by 4, it would equal 12/3 which will simplify to 3. This can be done again with 3*4=12.
So the answer would be 12*4 = 48 and 48*4 = 192.
Shivani runs a day care center. Of the 8 children at the day care center, 4 of them are six-year-olds. What is the probability that a randomly selected child will be a six-year-old? Write your answer as a fraction or whole number.
The probability that a randomly selected child will be a six-year-old is given by P ( A ) = 1/2
Given data ,
Let the probability that a randomly selected child will be a six-year-old be represented as P ( A )
Now , the total number of children in the day care = 8
The number of 6 year olds in the day care = 4
So , P ( A ) = number of 6 year olds in the day care / total number of children in the day care
On simplifying , we get
P ( A ) = 4/8
P ( A ) = 1/2
P ( A ) = 0.5
Hence , the probability is 1/2
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√
To the nearest minute, how many minutes
will it take to fill the balloon? Use 3.14
for T.
A. 129 minutes
B. 103 minutes
C. 181 minutes
D. 233 minutes
Where the radius of the ballon is given, the time taken to fill the balloon is: is 55.23 minutes or 55 minutes approximately.
What is the explanation for the above response?
The volume of a sphere is given by the formula:
V = (4/3)π³
V = Volume
r = Radius
Since the ballon is leaking at the rate of 26 cubic feet per minute, it means that the change of volue of the ballon is alow 26 cubic feet per minute.
If we replace the value for r (which is 7) in the above formula, we have:
V = (4/3) x 3.14 x 7³
V = 1436ft³
Thus, the time taken for the ballon to get empty is:
1436.03/26
= 55.23 mi
To the nearest minutes, that would be
55 minutes.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Air is leaking from a spherical-shaped advertising balloon at the rate of 26 cubic feet per minute. If the radius of the ball is 7 feet, to the nearest minute,how long would it take for the balloon to empty fully ? Round your answer to the nearest minute. Use the approximate of value of π, that is 3.14.
It is known that the population variance equals 484. With a 0.95 probability, the sample size that needs to be taken to estimate the population mean if the desired margin of error is 5 or less is a. 25 b. 74 c. 189 d. 75
The answer is d. 75. The sample size needed is approximately 189, which corresponds to option c.
To estimate the required sample size, we can use the formula:
n = (Z^2 * σ^2) / E^2
where:
Z = the Z-score associated with the desired level of confidence (0.95 = 1.96)
σ^2 = the population variance (484)
E = the desired margin of error (5)
Substituting these values, we get:
n = (1.96^2 * 484) / 5^2
n = 74.4096
Rounding up to the nearest integer, the required sample size is 75.
Therefore, the answer is d. 75.
To find the required sample size for estimating the population mean with a desired margin of error of 5 or less and a 0.95 probability, you can use the following formula:
n = (Z^2 * σ^2) / E^2
where n is the sample size, Z is the Z-score corresponding to the desired level of confidence (in this case, 0.95), σ^2 is the population variance, and E is the margin of error.
Given the population variance (σ^2) of 484 and a desired margin of error (E) of 5, we can use the Z-score for a 95% confidence level, which is 1.96. Plug these values into the formula:
n = (1.96^2 * 484) / 5^2
n ≈ 189
Therefore, the sample size needed is approximately 189, which corresponds to option c.
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when using your calculator, please indicate the function used and the parameters you entered for the function. 1. The selling prices of various homes in a community follow a normal distribution with a mean of $276,000.00 and standard deviation of $32,000.00. a. Calculate the probability that the next home in the neighborhood will sell for less than $220,000.00. Label the mean, standard deviation, and indicate the appropriate area on the included graph of a normal distribution. b. Calculate the probability that the next home in the community will sell for less than $350,000.00 but more than $250,000.00. Label the mean, standard deviation, and indicate the appropriate area on the included graph of a normal distribution.
On the graph of the normal distribution, we would label the mean as 276,000, the standard deviation as 32,000, and shade the appropriate area to represent the probabilities we calculated.
To calculate the probabilities, we will use the normal distribution function on the calculator. The parameters we will enter are the mean, standard deviation, and the values we are interested in finding the probability for.
a. To find the probability that the next home will sell for less than $220,000.00, we need to calculate the z-score first.
z-score = (220,000 - 276,000) / 32,000 = -1.75
Using the calculator, we will enter the function:
normdist(-1.75, 0, 1, TRUE)
where -1.75 is the z-score, 0 is the mean, 1 is the standard deviation, and TRUE indicates that we want to find the area to the left of the z-score.
The result is 0.0401, which means there is a 4.01% chance that the next home will sell for less than $220,000.00.
b. To find the probability that the next home will sell for less than $350,000.00 but more than $250,000.00, we need to calculate the z-scores for both values.
z-score for $350,000 = (350,000 - 276,000) / 32,000 = 2.31
z-score for $250,000 = (250,000 - 276,000) / 32,000 = -0.81
Using the calculator, we will enter the function:
normdist(2.31, 0, 1, TRUE) - normdist(-0.81, 0, 1, TRUE)
where 2.31 and -0.81 are the z-scores for $350,000 and $250,000 respectively, 0 is the mean, 1 is the standard deviation, and TRUE indicates that we want to find the area to the left of the z-scores.
The result is 0.3758, which means there is a 37.58% chance that the next home will sell for less than $350,000.00 but more than $250,000.00.
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pls solve with solution pls.
The first quartile for 1 - 3 is Q₁ = 756660.5 (b) The 5th decile for 5 - 6 is D5 = 2724770.5and (c) The 80th percentile for 7 - 9 is 775346.4
What is Quartile?Recall that a quartile is a statistical term used to measure the spread of values above and below the mean
the first quartile is represented by Q1
Q₁ = 1/4 (n+1)th term
Q₁ = 1/4 (3026641+1)
Q₁ = 3026642/4
Q₁ = 756660.5
b) The 5th decile can be calculated using the formula 5 (n+1) / 10, where 5 is the middle data point of any given set of numbers. This means that half of the scores lie above and below the distribution
This implies that D5 = 5 (n+1) / 10
D5 = 5(5449540 + 1) / 10
D5 = 5*5449541 /10
D5 = 27247705/10
D5 = 2724770.5
c) The 80th percentile is a measure of how well you are performing compared to other test takers.
It is calculated by dividing the number of points you scored by 100 and then multiplying that number by 50 to get an ordinal rank
the 80th % = n/100 * 80
80th percentile = 969183/100 * 80
80th Percentile = 969183 *80 = 775346.4
From the calculation, it means that Saudi Arabia has less cases of
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Which of the following describes the zeroes of the graph of f(x) = 3x6 + 30x5 +75x42
1
O-5 with multiplicity 2 and 3 with multiplicity 4
1
O 5 with multiplicity 2 and 3 with multiplicity 4
O-5 with multiplicity 2 and 0 with multiplicity 4
O 5 with multiplicity 2 and 0 with multiplicity 4
The function which describes the zeroes of the graph of f(x) = 3x6 + 30x5 +75x42 is 5 with multiplicity 2 and 3 with multiplicity 4, the correct option is B.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
Linear function is a function whose graph is a straight line
We are given that;
The function f(x) = 3x6 + 30x5 +75x42
Now,
We can factorize f(x) = 3x6 + 30x5 +75x4 by taking out the common factor of 3x4:
f(x) = 3x4(x2 + 10x + 25)
Then we can factorize the quadratic expression inside the parentheses by finding two numbers that multiply to 25 and add to 10. These numbers are 5 and 5, so we have:
f(x) = 3x4(x + 5)(x + 5)
To find the zeroes, we set f(x) equal to zero and solve for x:
0 = 3x4(x + 5)(x + 5)
This equation has two solutions: x = 0 and x = -5. However, x = 0 is a zero of multiplicity 4, because it makes x4 equal to zero four times. Similarly, x = -5 is a zero of multiplicity 2, because it makes (x + 5) equal to zero twice.
Therefore, by the function the answer will be 5 with multiplicity 2 and 3 with multiplicity 4
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To graph the inequality y ≤ -6x-8, you would draw a dashed line.
OA. True
O
B. False
What is the yield on a corporate bond with a $1000
face value purchased at a discount price of $850, if
it pays 8% fixed interest for the duration of the
bond?
yield = [?] %
Give your answer as a percent rounded to the nearest
hundredth.
The yield on a corporate bond is A = 9.14 %
Given data ,
Face value of the bond (FV) = $1000
Purchase price of the bond = $850
Fixed interest rate = 8%
The annual interest payment (I) can be calculated as a percentage of the face value:
I = (Fixed interest rate / 100) * FV
Substituting the given values:
I = (8 / 100) x 1000 = $80
The yield (Y) can be calculated as:
Y = (Annual interest payment / Purchase price) * 100
Substituting the calculated values:
Y = (80 / 850) x 100 = 9.41%
Hence , the yield on the corporate bond is 9.41%
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Write an equivalent expression to x-4y+9
Answer:
Step-by-step explanation:
you could break up a term, like the y term.
x+2y+2y+9 this is equivalent
9. Name the four basic logic gates.
The four basic logic gates are AND, OR, NOT, and XOR.
1. AND Gate: This gate takes two or more inputs and produces an output of 1 (true) only if all the inputs are 1 (true).
2. OR Gate: This gate takes two or more inputs and produces an output of 1 (true) if at least one of the inputs is 1 (true).
3. NOT Gate (Inverter): This gate has only one input and inverts it, producing an output of 1 (true) if the input is 0 (false) and vice versa.
4. XOR Gate (Exclusive OR): This gate takes two inputs and produces an output of 1 (true) if either, but not both, of the inputs are 1 (true).
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used in case-control studies, a type of indirect measure of the association between frequency of exposure and frequency of outcome is known as the: group of answer choices odds ratio population risk difference attributable risk all of these are correct.
In case-control studies, the indirect measure of association between frequency of exposure and frequency of outcome is known as the odds ratio.'
The answer to your question is odds ratio. In case-control studies, odds ratio is used as an indirect measure of the association between frequency of exposure and frequency of outcome. It compares the odds of exposure in cases to the odds of exposure in controls, and provides an estimate of the strength of the association between exposure and outcome. While other measures such as population risk difference and attributable risk may also be calculated in case-control studies, odds ratio is the most commonly used measure of association.
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Find the critical value t Subscript c for the confidence level c=0.98 and sample size n=24
The critical value t Subscript c for a confidence level of 0.98 and sample size of 24 is 2.500.
To find the critical value t Subscript c for the confidence level c=0.98 and sample size n=24, we can use a t-distribution table or calculator.
Since we have a sample size of n=24, we have n-1 = 23 degrees of freedom. Using a t-distribution table or calculator with 23 degrees of freedom and a confidence level of 0.98, we get
t Subscript c = 2.500
Therefore, the critical value t Subscript c for the confidence level c=0.98 and sample size n=24 is 2.500. This means that if we calculate the t-value from our sample data and it is greater than or less than 2.500 in absolute value, we can reject the null hypothesis at the 0.02 level of significance.
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6. an economics researcher wants to estimate the mean number of hours worked by all grocery store employees in the county. how many employees must be included in the sample to be 95% confident that the sample mean is within 1.5 hours of the population mean? a previous study showed that the population standard deviation is 7.9. the critical value for a level of confidence of 95% is 1.96.
The number of employees that must be included in the sample to be 95% confident that the sample mean is within 1.5 hours of the population mean is 107 employees.
To estimate the mean number of hours worked by all grocery store employees in the county with 95% confidence and a margin of error of 1.5 hours, we can use the sample size formula:
n = (Z * σ / E)²
where:
- n is the required sample size
- Z is the critical value (1.96 for a 95% level of confidence)
- σ is the population standard deviation (7.9 from the previous study)
- E is the margin of error (1.5 hours)
Plugging in the given values:
n = (1.96 * 7.9 / 1.5)²
n ≈ 106.56
Since you cannot have a fraction of an employee, you need to round up to the nearest whole number. Therefore, the researcher must include 107 employees in the sample to be 95% confident that the sample mean is within 1.5 hours of the population mean.
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