The 90% confidence interval is from −11.447 to −5.913.
Given that: Sample size of fraud, n1 = 26
Sample size of firearms, n2 = 35
Sample mean of fraud, x1 = 8.94 months
Sample mean of firearms, x2 = 17.62 months
Sample standard deviation of fraud, s1 = 3.87 months
Sample standard deviation of firearms, s2 = 4.12 months T
he two samples are independent
We need to find the 90% confidence interval for the difference between the mean times served by prisoners in the fraud and firearms offense categories. Now, the point estimate of the difference in means of two populations is:
x1 − x2 = 8.94 − 17.62 = −8.68
Using the pooled t-interval formula, we get:
[8.68 − tα/2 × Sp(1/n1 + 1/n2), 8.68 + tα/2 × Sp(1/n1 + 1/n2)]
Here, the degrees of freedom is df = n1 + n2 - 2 = 59 at the 0.10 level of significance. tα/2 = t0.05 = 1.671,
from t-distribution table Pooled variance Sp
= [(n1 - 1) × s1² + (n2 - 1) × s2²] / (n1 + n2 - 2)= [(26 - 1) × 3.87² + (35 - 1) × 4.12²] / (26 + 35 - 2)≈ 17.07
Therefore, the 90% confidence interval is given as follows:
[8.68 - 1.671 × (sqrt(17.07) × sqrt(1/26 + 1/35)), 8.68 + 1.671 × (sqrt(17.07) × sqrt(1/26 + 1/35))]=[−11.447, −5.913] (rounded to three decimal places)
Hence, the required confidence interval is from −11.447 to −5.913.
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I need so much help please save me
Answer:
Step-by-step explanation:
One of the Answers is C
0.75x — 13 = 2
What's the value of x
Answer:
The value of x is 20.
Step-by-step explanation:
The steps are :
0.75x - 13 = 2
0.75x = 2 + 13
0.75x = 15
x = 15 ÷ 0.75
x = 20
find the z value for 0.99 if e O¨zlem likes jogging 3 days of a week. She prefers to jog 3 miles. For her 95 times, the mean wasx¼ 24 minutes and the standard deviation was S¼2.30 minutes. Let μ be the mean jogging time for the entire distribution of O¨zlem’s 3 miles running times over the past several years. How can we find a 0.99 confidence interval for μ?.
likes jogging 3 days of a week. She prefers to jog 3 miles. For her 95 times, the mean wasx¼ 24 minutes and the standard deviation was S¼2.30 minutes. Let μ be the mean jogging time for the entire distribution of O¨zlem’s 3 miles running times over the past several years. How can we find a 0.99 confidence interval for μ
a) What is the table value of Z for 0.99? (Z0.99)? (b) What can we use for σ ? (sample size is large) (c) What is the value of? Zcσffiffin p (d) Determine the confidence interval level for μ.
a. The table value of z 0.99 is given as 2.58.
b. we use σ = 2.30 minutes.
c. The value of Z is given as 0.609.
d. The confidence interval is (23.391, 24.609) minutes.
How to solve for the z critical valuea) To find the z-score for a 0.99 confidence interval, we need to find the z-score that leaves 0.5% (since it's two-tailed, we split the 1% or 0.01 of the data that's not within the confidence interval into two) in each tail. The z-score for 0.995 (0.5% in the upper tail) is approximately 2.58 in standard normal distribution tables. So, Z_0.99 is 2.58.
b) Therefore, we use σ = 2.30 minutes.
c) The standard error of the mean (SE) is given by σ/√n, where n is the sample size.
Here, σ = 2.30 minutes and n = 95.
Therefore, SE = σ/√n
= 2.30/√95
= 0.236 minutes.
Multiply this by the z-score to find Z * σ/√n.
Therefore, Z * σ/√n = 2.58 * 0.236 ≈ 0.609.
d) The 0.99 confidence interval for μ
Here, x is the sample mean which is 24 minutes.
So the confidence interval is approximately
= (24 - 0.609, 24 + 0.609)
= (23.391, 24.609) minutes.
This is the range of values we are 99% confident that the true population mean (μ) falls in.
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What is the measure of angle C?
45°
с
35
B
A 10°
B
80°
C 100°
D
180°
Answer:
100°
since being sum of angles of triangle
30 POINTS + BRAINLIEST TO FIRST CORRECT ANSWER!
The ratio table below shows the relationship between the number of bricks in a wall and the length of the wall.
Brick Wall
Number of bricks Length (ft)
6 3
8 4
12 6
18 9
When the number of bricks is multiplied by 2, the length is multiplied by
1.
2.
3.
6.
Answer:
The length will be multiplied by 2.
Step-by-step explanation:
By looking at the first and third ratio, we know that the no. of birck have been multiplied by 2 and the length has also been multiplied by 2 .
So when the number of bricks is multiplied by 2, the length is multiplied by 2
Answer:
2Step-by-step explanation:
Using the table we observe the points
(6, 3) and (12, 6)The number of bricks doubled
6*2 = 12, andThe length is doubled accordingly
3*2 = 6So the answer is 2
1)A factory makes propeller drive shafts for ships. A quality assurance engineer at the factory needs to estimate the true mean length of the shafts. She randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. The lengths are known to follow a normal distribution whose standard deviation is 2 mm. Calculate a 95% confidence interval for the true mean length of the shafts. Input your answers for the margin of error, lower bound, and upper bound.
a)Determine Margin of Error for this 95% confidence interval.
b)Input the lower bound. (Round to three decimal places)
c)Input the upper bound. (Round to three decimal places)
2)To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly weighed a total of n times and the mean of the weighings is computed. Suppose the scale readings are normally distributed with unknown mean μ and standard deviation σ = 0.01 g. How large should n be so that a 95% confidence interval for μ has a margin of error of ± 0.0001?
3)A medical researcher is working on a new treatment for a certain type of cancer. The average survival time after diagnosis for the standard treatment is two years. So the null hypothesis is that average survival time after diagnosis is the same for the new treatment and the standard treatment.
In an early trial, she tries the new treatment on three subjects, who have an average survival time after diagnosis of 4.5 years. Even though the sample is small, the results are statistically significant at the 0.05 significance level. Consequently, she rejects the null hypothesis.
In a future study, it is determined that the new treatment does not increase the mean survival time in the population of all patients with this particular type of cancer. The researcher has
Committed a type I error.
Incorrectly used a 0.05 significance test when she should have computed the P-value.
Incorrectly used a 0.05 significance level when she should have used a 0.01 significance level.
Committed a type II error.
4)If the level of significance, α{"version":"1.1","math":"\alpha"}, is made very small, thereby making the probability of committing a Type 1 error very small, what happens to the probability of committing a Type 2 error?
By reducing the probability of committing a Type 1 error, we increase the probability of committing a Type 2 error.
There is no specific relationship between the two probabilities.
By reducing the probability of committing a Type 1 error, we also reduce the probability of committing a Type 2 error.
The relationship between the two probabilities depends on how the study is set up.
Therefore, with a 95% confidence interval, we can estimate the true mean length of the drive shafts to be between 992.16 mm and 1007.84 mm.
The true mean length of the drive shafts can be estimated using a 95% confidence interval. The margin of error is calculated as 2*1.96*2 = 7.84 mm. The lower bound of the confidence interval is 1000 - 7.84 = 992.16 mm and the upper bound is 1000 + 7.84 = 1007.84 mm.
This confidence interval states that there is a 95% probability that the true mean length of the drive shafts falls within the range of 992.16 mm to 1007.84 mm. The relationship between the two probabilities is that the probability of the true mean length falling within the confidence interval is 95%. If the sample size was increased, the margin of error would decrease, resulting in a tighter range and higher probability that the true mean would fall within the confidence interval.
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I need the answer for this question
Answer:
B
Step-by-step explanation:
When performing a statistical test, such as the Chi-Square test, what p-value indicates that the data differ significantly from that expected if the null hypothesis is true?
When performing a statistical test, such as the Chi-Square test, the p-value is a crucial component in determining the significance of the data compared to the null hypothesis. The p-value represents the probability of observing the given data, or more extreme results, assuming the null hypothesis is true. In general, a p-value threshold of 0.05 is used to determine statistical significance.
If the calculated p-value is less than or equal to 0.05, it indicates that the observed data significantly differ from what is expected under the null hypothesis. This means that there is a less than 5% chance of obtaining the observed data if the null hypothesis were true. Consequently, researchers often reject the null hypothesis in favor of the alternative hypothesis when the p-value is less than or equal to 0.05.
However, it is essential to note that the choice of the significance level is subjective and may vary depending on the field or specific study. In some cases, a more stringent threshold, such as 0.01, might be required to minimize the chances of false positives, while in other situations, a more lenient threshold, such as 0.10, may be acceptable.
In summary, a p-value of 0.05 or less typically indicates that the data differ significantly from what is expected under the null hypothesis in a statistical test like the Chi-Square test. However, the chosen threshold for significance may vary depending on the specific context and research objectives.
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4. Lana has a bag of marbles. The probability of picking a striped marble is 8%. If Lana picks a marble and then replaces it 320 times, predict about how many times she would pick a marble that is not striped.
Lana would pick a non-striped marble about 294 times.
The probability of picking a marble that is not striped is 100% - 8% = 92% = 0.92. This means that for each pick, the probability of getting a non-striped marble is 0.92.
If Lana picks a marble and replaces it 320 times, the number of times she would pick a non-striped marble can be predicted by multiplying the probability of getting a non-striped marble by the number of picks.
So, the number of times she would pick a non-striped marble is:
0.92 x 320 = 294.4
Rounding to the nearest whole number = 294.
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If you were constructing a 99% confidence interval of the population mean based on a sample of n=30 where the standard deviation of the sample S=0.05, the critical value of t will be 2.7564 2.4922 2.7969
The critical value of t for constructing a 99% confidence interval with a sample size of 30 and a sample standard deviation of 0.05 is 2.7564.
A confidence interval is a range of values within which the population parameter is estimated to lie with a certain level of confidence. In this case, we are constructing a 99% confidence interval for the population mean. The critical value of t is used to determine the width of the confidence interval.
The formula for calculating the confidence interval for the population mean is:
Confidence interval = sample mean ± (critical value) * (standard deviation of the sample / square root of the sample size)
Given that the sample size is 30 (n = 30) and the standard deviation of the sample is 0.05 (S = 0.05), we need to find the critical value of t for a 99% confidence level. The critical value of t depends on the desired confidence level and the degrees of freedom, which is equal to n - 1 in this case (30 - 1 = 29). Looking up the critical value in a t-table or using statistical software, we find that the critical value of t for a 99% confidence level with 29 degrees of freedom is approximately 2.7564.
Therefore, the 99% confidence interval for the population mean would be calculated as follows: sample mean ± (2.7564) * (0.05 / √30). The final result would be a range of values within which we can be 99% confident that the true population mean lies.
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the equation: 3(x - 1) = 2x + 9
Answer:
x = 12
Step-by-step explanation:
mark as brainlist pls
Answer:
X= 12
Step-by-step explanation:
Type the correct answer in each box.
Consider the expressions shown below.
-7z²
Complete each of the following statements with the letter that represents the expression.
-
-
2x + 5 7x²
B
C
- 2x + 7 7z² + 2x
-
(32²6z+11) - (10z² - 4z + 6) is equivalent to expression
(-32² - 5z-3) - (-102²-7z+ 2) is equivalent to expression
(12z² + 6z-5) - (5z² + 8z 12) is equivalent to expression
5
We can see here that:
(3z² - 6z + 11) - (10z² - 4z + 6) is equivalent to expression A.
(-3z² - 5z - 3) - (-10z²- 7z + 2) is equivalent to expression C.
(12z² + 6z - 5) - (5z² + 8z - 12) is equivalent to expression B.
What are mathematical expressions?Mathematical expressions are combinations of numbers, variables, symbols, and mathematical operations that represent a mathematical relationship or equation. They are used to describe and solve mathematical problems in a concise and systematic way.
We can actually see here that:
Expanding (3z² - 6z + 11) - (10z² - 4z + 6) will give us:
3z² - 6z + 11 - 10z² + 4z - 6 = -7z² - 2z = 5 thus equal to expression A.
The same expansion method will reveal others too.
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Triangle properties
6(kx+3)-12kx=25+6k. Solve the equation below for x in terms of k
Answer:k=-7/6x+6
Step-by-step explanation: \(6kx+18-12kx=25+6k\) We use the distributive property first. Then combine like terms. -6xk+18-6k=25
factor it out (-6x-6)k=7 and divided (-6x-6) on both side.
Then our final answer is k=-7/6x+6
Find the critical numbers of the function on the interval 0≤ θ < 2π.
f(θ) = 2cos(θ) +(sin(θ))^2
Critical values of the function f(θ) = 2cos(θ) +(sin(θ))² on the interval 0≤ θ < 2π is 0 and π.
Therefore, the answer is 0 and π.
f(θ) = 2cos(θ) +(sin(θ))²
f'(θ) = -2sin(θ) +2sin(θ)cos(θ)
Critical values of f are points at which f' is zero or not defined.
For all values of θ, we can find that f'(θ) is defined.
f'(θ) = 0
-2sin(θ) +2sin(θ)cos(θ) = 0
cos(θ) - 1 = 0 or sin(θ) = 0
cos(θ) = 1
θ = nπ, n = 0, 1, 2, ...
sin(θ) = 0
θ = nπ, n = 0, 1, 2, ...
Therefore in the interval 0 ≤ θ < 2π, critical values are 0 and π.
2π is not there as it is not included in the interval.
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Oatmeal is packaged in a right circular cylindrical container that has a radius of 1.5 inches and a height of 12 inches. What is the surface area of this container in terms of π?
Answer:
= 40.5π square inches
Step-by-step explanation:
Oatmeal is packaged in a right circular cylindrical container that has a radius of 1.5 inches and a height of 12 inches. What is the surface area of this container in terms of π?
The formula for the surface Area of a cylinder = 2πr( r + h)
r = 1.5 inches
h = 12 inches
Hence,
2 × π × 1.5( 1.5 + 12)
3π(13.5)
= 40.5π square inches
The surface area of the cylinder is
= 40.5π square inches
If you want to know the answer to this question, "What shape has 1 pair of opposite sides parallel?" it's "TRAPEZOID"
A trapezoid is a shape with one set of opposing sides that are parallel.
As we know that a trapezoid is a quadrilateral with one parallel set of sides.
These parallel sides are known as the trapezoid's bases, and they can be of varying lengths. The legs are the other two sides of the trapezoid. The other leg is not parallel to the other base.
A trapezoid's parallel sides are commonly labeled as base 1 and base 2, while the legs are labeled as side 1 and side 2.
A trapezoid's height is the perpendicular distance between its bases.
Therefore, it is a trapezoid.
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There are 6 mice in an attic. Their population is growing at a rate of12% per month.a. Write an exponential growth function to model this situation.
general equation of a population is
\(y=a(1+\frac{b}{100})^x\)where a is the initial population and b the percent of growing
then replacing a=6 and b=12
\(y=6(1+\frac{12}{100})^x\)and simplify
\(\begin{gathered} y=6(1+0.12)^x \\ y=6(1.12)^x \end{gathered}\)State the slope and y-intercept of the graph of the equation y = 3x + 2
The slope is _________.
The y-intercept is ____________-
Find the length of an arc of a circle with a 12-cm radius associated with a central angle of 135 degrees. Give your answer in exact and approximate form to the nearest hundredth. Show and explain your work
The length of the arc is 28. 26 cm
How to determine the lengthFirst, we need to know that the formula for calculating the length of an arc is expressed as;
L = 2πr × θ/360
Such that r is the radius and θ is the degree
Now, substitute the value, we get;
Length = 2 × 3.14 × 12 × 135/360
Multiply the values, we have;
Length = 75. 36 × 135/360
Divide the values, we get;
Length = 75. 36 × 0. 375
Multiply the values, we get;
Length = 28. 26 cm
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A stadium brought in an average revenue of $11,000 per night for a professional sports tournament. Total receipts for the
period of time the tournament took place was $132,000. This means the tournament took place throughout how many days?
a) 5
b) 7
c) 12
d) 14
A stadium brought in an average revenue of $11,000 per night for a professional sports tournament. Total receipts for the period of time the tournament took place was $132,000. This means the tournament took place throughout is 12 days
How to find the number of members ?
When the teachers joined the members of the chess club for a tournament, the number of members that Alan counted was 31 people which means that the number of members in the chess club would be this number, less the number of teachers.
A stadium brought in an average revenue of $11,000 per night for a professional sports tournament.
Total receipts for the period of time the tournament took place was $132,000.
This means the tournament took place throughout how many days?
since total divide by per night is equal to number of days
now 132000/11000= 12
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3x + y = -8 -2x - y = 6
Answer:
x=-2
Step-by-step explanation:
if we find sum of same variables ,
3x-2x+y-y=-8+6
x=-2
How do you find the inverse tangent?
To find the inverse tangent of a number or ratio, you can use a scientific calculator or mathematical tables. Alternatively, you can use the tangent function and a calculator or table to find the angle whose tangent is equal to the ratio, then write "tan⁻¹" followed by the ratio to indicate the inverse tangent.
To find the inverse tangent, also known as the arctangent, of a number or ratio, you can use a scientific calculator or mathematical tables.
However, if you need to find the inverse tangent by hand, you can use the following steps:
Write down the ratio for which you want to find the inverse tangent.
Determine the angle whose tangent is equal to the ratio by using the tangent function, which is the reciprocal of the tangent function.
Use a calculator or a table to find the angle whose tangent is equal to the ratio.
Round the angle to the nearest degree, if necessary.
Write "tan⁻¹" followed by the ratio or number to indicate that you have found the inverse tangent.
For example, to find the inverse tangent of 1, you would use the formula "tan⁻¹(1)" and determine that the angle whose tangent is equal to 1 is 45 degrees. Therefore, the inverse tangent of 1 is equal to 45 degrees, or "tan⁻¹(1) = 45°".
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a graph that would indicate whether there was a negative relationship between stock and bond returns would be: group of answer choices frequency distribution pareto chart of both stock and bond returns scatter plot bar chart age of parents, college education, past vacations
A scatter plot would be the best choice to indicate whether there was a negative relationship between stock and bond returns.
What is scatter plot?A scatter plot is a type of graph used to display the relationship between two variables. It is also known as a scatter chart or scattergram. The graph consists of a series of points, each representing a single observation or measurement of two variables. The position of each point is determined by its values on the two variables. In a scatter plot, one variable is plotted on the x-axis and the other variable is plotted on the y-axis.
This type of graph would show the relationship between two variables, in this case stock and bond returns, on a single graph. It would provide a visual representation of any negative or positive correlation between the two variables.
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h(x) = 4x +3. What is
the coordinate pair for h (1)?
9514 1404 393
Answer:
(1, 7)
Step-by-step explanation:
Fill in x=1 and do the arithmetic.
h(1) = 4(1) +3 = 7
The coordinate pair is ...
(x, h(x)) = (1, h(1)) = (1, 7)
PLEASE HELP SOMEBODY!
Answer:
C. As the fat increases, the calories increase too
Answer:
c
Step-by-step explanation:
Hailey ran a few laps. D(n)D(n)D, (, n, )models the duration (in seconds) of the time it took for Hailey to run her n^{th}n th n, start superscript, t, h, end superscript lap. nnn 333 777 999 D(n)D(n)D, (, n, )858585 999999 110110110 When did the lap duration increase faster
Question:
Hailey ran a few laps. D(n), models the duration (in seconds) of the time it took for Hailey to run her nth lap. When did the lap duration increase faster?
A. Between the 3rd and 7th lap
B. Between the 7th and 9th lap
C. The lap duration increased at the same rate over both intervals
Answer:
B. Between the 7th and 9th lap
Step-by-step explanation:
Given
See attachment for table
Required
Determine when the lap increases faster
To do this, we simply calculate the rate of change between each lap.
From the attachment, we have:
\(D(3) = 85\)
\(D(7) = 99\)
\(D(9) = 110\)
Rate of change is calculated using:
\(Rate = \frac{D(b) - D(a)}{b - a}\)
For D(3) to D(7), the rate is:
\(Rate = \frac{D(7) - D(3)}{7 - 3}\)
\(Rate = \frac{99 - 85}{7 - 3}\)
\(Rate = \frac{14}{4}\)
\(Rate = 3.5\)
For D(7) to D(9), the rate is:
\(Rate = \frac{D(9) - D(7)}{9 - 7}\)
\(Rate = \frac{110 - 99}{9 - 7}\)
\(Rate = \frac{11}{2}\)
\(Rate = 5.5\)
The rate of change between the 7th and 9th lap is greater than the rate of change between then 3rd and 7th lap .
Hence, (b) is correct
Answer:
B) Between the 7th lap and the 9th lap
Step-by-step explanation:
⦁ The data set shows the number of practice throws players in a basketball competition made and the number of free throws they made in a timed competition. Practice throws 4 10 6 15 0 7 11 Free throws 8 23 9 34 5 11 27 ⦁ ⦁ Use technology to find the equation and coefficient of determination for each type of regression model. Use the number of practice throws for the input variable and the number of free throws for the output variable. Round all decimal values to three places. Model Equation of regression model Coefficient of determination Linear Quadratic Exponential (standard form) ⦁ ⦁ Which model best fits the data set? Explain. Answer:
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
Practice throws(X) : 4 10 6 15 0 7 11
Free throws(Y) : 8 23 9 34 5 11 27
Using the online linear regression calculator :
ŷ = 2.1559X + 0.3912
2.1559 = slope
0.3912 = intercept
X = independent variable ; y = dependent variable
The Coefficient of determination (R²) = 0.9506² = 0.9036
Quadratic model : y = 0.0961x²+0.7138x+3.8031
Coefficient of determination(R²) = 0.9739² = 0.9485
Exponential model:
a*b^x
Coefficient of determination (R²) = 0.9753² = 0.9512
The exponential model fits the data best.
I WILL GIVE BRAINLIEST!!!
Please help me.
Translate all word problems into equations.
You only need to give equation+answer for number 7 and 9.
7. Between noon and midnight, the temperature
dropped 20°F. If the temperature was -8°F at
midnight, what was the temperature at noon?
8. If a strawberry pie is divided into 6 equal slices, each
slice has 240 calories. How many calories are in the
whole pie?
9. A chest was resting on the ocean floor 1000 ft below
the surface. It was lifted to the deck of a ship 8 ft
above the surface. How far was the chest lifted?
10. When all the kids who tried out for Little League
were divided into teams of 20 players, there were
exactly 8 teams. How many kids tried out?
Step-by-step explanation: They are word problems into equations. Have a good night. you will get them right.
7.) x - 20 = -8
8.) x/6 = 240
9.) - 1000 + x = 8
10.) x/20 = 8
12 cm
8 cm
5 cm
5 cm
17 cm
26. The area of the composite figure above is_cm-square.
1 point
Your answer