Answer:
Step-by-step explanation:
This problem could keep you going for quite a while. My suggestion is that you go get a cup of coffee and sip it slowly as you read this.
Equation One
Sqrt(x - 1)^3 = 8
(x - 1)^(3/2) = 8
Square both sides to get rid of the 2.
(x - 1)^3 = 8^2
(x - 1)^3 = 64
Now take the cube root of both sides to get rid of the 3 on the left
x - 1 = cuberoot(64)
x - 1 = 4 Add 1 to both sides
x - 1+1 = 4 + 1
x = 5
==============================
Second Equation
4th root (x - 3)^5 = 32
Take the 5th root of both sides.
4th root(x - 3) = 2
This can be written as (x - 3)^(1/4) = 2
Now take the 4th power of both sides.
(x - 3) = 2^4
x - 3 = 16
add 3 to both sides.
x = 16 + 3
x = 19
============================
Equation 3
(x - 4)^(3/2) = 125
Take the cube root of both sides
(x - 4)^(1/2) = 125^(1/3) 1/3 is the cube root of something
(x - 4)^(1/2) = 5
square both sides to get rid of the 2
(x - 4) = 5^2
x - 4 = 25
Add 4 to both sides.
x = 25 + 4
x = 29
============================
Fourth Equation
(x + 2)^(4/3) = 16
take the 4th root of both sides
(x + 2) ^(1/3) = 16^(1/4)
(x + 2)^(1/3) = 2
Cube both sides
(x + 2) = 2^3
x + 2 = 8
Subtract 2 from both sides
x + 2 - 2 = 8-2
x = 6
##########################
The first step is the most critical. You must look at what you are going to take the root of. When you do, for this question, it must come out even.
Researchers want to determine if caffeine affects reaction time. They divide a sample of 150 people into 3 groups. Group 1 gets a regular drink with no caffeine, group 2 gets a drink with 95 mg of caffeine, and group 3 gets a drink with 250 mg of caffeine. Each group is then given a test to gauge their reaction time. What is the appropriate test to use?
Answer:
One-way ANOVA
Step-by-step explanation:
One-way ANOVA(analysis of variance) a testing method in statistics that is used to compare the means of two or more independent samples, to check if the differences are statistically significant.
In this case, we have three groups which their various reaction time to caffeine is to be tested using the same testing method (amount of caffeine). Hence the appropriate test to use here is the one-way ANOVA
The production department has installed a new spray machine to paint automobile doors. As is common with most spray guns, unsightly blemishes often appear because of improper mixtures or other problems. A worker counted the number of blemishes on each door. Most doors had no blemishes; a few had one; a very few had two; and so on. The average number was 0.5 per door. The distribution of blemishes followed the Poisson distribution. Out of 10,000 doors painted, about how many would have no blemishes
Answer:
The numbers of doors that will have no blemishes will be about 6065 doors
Step-by-step explanation:
Let the number of counts by the worker of each blemishes on the door be (X)
The distribution of blemishes followed the Poisson distribution with parameter [tex]\lambda =0.5[/tex] / door
The probability mass function on of a poisson distribution Is:
[tex]P(X=x) = \dfrac{e^{- \lambda } \lambda ^x}{x!}[/tex]
[tex]P(X=x) = \dfrac{e^{- \ 0.5 }( 0.5)^ x}{x!}[/tex]
The probability that no blemishes occur is :
[tex]P(X=0) = \dfrac{e^{- \ 0.5 }( 0.5)^ 0}{0!}[/tex]
[tex]P(X=0) = 0.60653[/tex]
P(X=0) = 0.6065
Assume the number of paints on the door by q = 10000
Hence; the number of doors that have no blemishes is = qp
=10,000(0.6065)
= 6065
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
81.64
Step-by-step explanation:
To find the circumference of this circle we take pi or 3.14 and multiply it by 2
3.14 * 2 = 6.28
Then we multiply 6.28 by 13
6.28 * 13 = 81.64
Find the following measure for this figure.
Volume =
Answer:
91 2/3 pi cubic units
Step-by-step explanation:
The formula for the volume of cone is [tex]\dfrac{1}{3}\pi r^2 h[/tex]. Plugging in the given numbers, you get:
[tex]\dfrac{1}{3}\cdot \pi \cdot 5^2 \cdot 11= 91 \ 2/3 \pi[/tex]
Hope this helps!
Answer:
[tex]Volume=\frac{1}{3} \,275\,\pi[/tex] cubic units
Notice that this answer doesn't agree with any of the first three in the list provided via the screenshot
Step-by-step explanation:
Recall the formula for the volume of a cone:
[tex]Volume=\frac{1}{3} Base\,*\,Height[/tex]
In this case the Height is 11 units, and they also give us the radius of the circular base (5 units) from which we can find the circle's base area:
[tex]Area_{circle} = \pi\,R^2\\Area_{circle}=\pi\,(5)^2\\Area_{circle}=25 \pi[/tex]
therefore the total volume becomes:
[tex]Volume=\frac{1}{3} Base\,*\,Height\\Volume=\frac{1}{3} 25\,\pi\,*\,11\\\\Volume=\frac{1}{3} \,275\,\pi[/tex]
Develop a 3-week moving average for the following time series Time PeriodTime Series Value 19 22 39 416 511 62 77 Find the value for MSE. Round your calculations to 2 decimal places.
Answer:
MSE = 198.18 / 3 = 66.06
Step-by-step explanation:
Time period : Time series value
1 : 9
2 : 2
3 : 9
4 : 16
5 : 11
6 : 2
7 : 7
3 weeks moving average
F4 = average of weeks 1-3 = ( 9 + 2 + 9 ) / 3 = 20 / 3 = 6.67
F4 = average of weeks 2-4 = ( 2 + 9 + 16 ) / 3 = 27 / 3 = 9
F4 = average of weeks 3-5 = ( 9 + 16 + 11 ) / 3 = 36 / 3 = 12
F4 = average of weeks 4 - 6 = ( 16 + 11 + 2 ) / 3 = 9.67
attached is the table showing the development of the 3-week moving average
the answer is 15 hours what is the question
Answer:
how many hours do you spend on your laptop
Answer:
the question is 17 hours - 2 hours
PLEASE ANSWER FAST !!!
What is the range of the function g for given domain ?
Answer:
The answer is B
Step-by-step explanation:
Hope this helps.. if not im sorry :(
What is the surface area of the pyramid? 12ft 10ft 10ft
Answer:
2h x (l+b)
2x10 X (12+10)
20 X 22
44 cm cube is your answer...
4
What is tan 11pi/6
Answer:
[tex]tan(\frac{11\pi}{6}) =-\frac{\sqrt{3} }{3}[/tex]
Step-by-step explanation:
Notice that [tex]\frac{11\pi}{6}[/tex] is an angle in the fourth quadrant (where the tangent is negative), and the angle is in fact equivalent to [tex]-\frac{\pi}{6}[/tex]. This is one of the special angles for which the sine and cosine functions, as well as the tangent function have well know values:
Recall that the tangent is defined as
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
and for this angle ( [tex]\frac{11\pi}{6}[/tex] ) the value of the sine and cosine functions are well known:
[tex]sin (\frac{11\pi}{6}) =-\frac{1}{2} \\cos( \frac{11\pi}{6}) =\frac{\sqrt{3} }{2}[/tex]
Then, the tangent would be:
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}\\tan(\frac{11\pi}{6}) = \frac{-\frac{1}{2} }{\frac{\sqrt{3} }{2} } \\tan(\frac{11\pi}{6}) =-\frac{1}{\sqrt{3} } \\tan(\frac{11\pi}{6}) =-\frac{\sqrt{3} }{3}[/tex]
what is the slope of the line that is parallel to the line y= 3/4x + 2
Answer:
3/4
Step-by-step explanation:
Answer:
3/4
Step-by-step
Since they are parallel they will have the same slope but not the same intercept
angle ∠DAC= angle ∠BAD. What is the length of BD? Round to one decimal place.
Answer: 3.9
Step-by-step explanation: Khan Academy
The length of BD if The angle ∠ DAC is equal to the angle ∠ BAD is 3.92.
What is the triangle?Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.
Given:
The angle ∠ DAC = angle ∠ BAD
As we can see that the triangle BAD and triangle DAC are similar By SAS similarity,
AC / AB = CD / BD (By the proportional theorem of similarity)
5.6 / 5.1 = 4.3 / BD
1.09 = 4.3 / BD
BD = 4.3 / 1.09
BD = 3.92
Thus, the length of BD is 3.92.
To know more about Triangles:
https://brainly.com/question/16886469
#SPJ2
Diana works in a building that is 130 feet tall. She is outside, looking up at the building at an angle of 37° from her feet to the top of the building. If Diana walks forward and her angle looking to the top of the building changes to 40°, how much closer is she to the building? Round the answer to the nearest tenth of a foot.
Answer:
Let x be her initial distance from the building, then tan 37 = 130/x
x = 130/tan 37 = 130/0.7536 = 172.5 feet
Let y be her distance from the building after moving forward, then
tan 40 = 130/y
y = 130/tan 40 = 130/0.8391 = 154.9
After moving forward, she is 172.5 - 154.9 = 17.6 ft closer.
Answer: B. 17.6 ft.
Step-by-step explanation: I just did it on the edge 2023 assignment. Check attached image.
A sample of 75 information systems managers had an average hourly income of $40.75 with a standard deviation of $7.00. The 95% confidence interval for the average hourly wage (in $) of all information system managers is
Answer:
The 95% confidence interval for the average hourly wage of all information system managers is (39.14,42.36)
Step-by-step explanation:
In order to calculate the 95% confidence interval for the average hourly wage we would have to calculate first the margin of error as follows:
ME=t0.05/2,n-1s/√n
for n=75, t0.025,74=1.993
Therefore, ME=1.993*7/√75
ME=1.61
Therefore, the 95% confidence interval for the average hourly income of all syatem manager would be as follows:
(X-ME,X+ME)=(40.75-1.61,40.75+1.61)
=(39.14,42.36)
help plz!!!! 30 points!!!!!!!!!! i will mark brainliest for who answers first! anveer bought 0.7 pounds of sliced ham at his local deli. If the deli charged $6.79 per pound, how much did Tanveer pay? A. $2.04 B. $4.75 C. $7.49 D. $9.70
Answer:
B
Step-by-step explanation:
[tex]6.79 \times 0.7[/tex]
[tex]=4.753[/tex]
Answer:
The correct answer would be $4.75
Step-by-step explanation:
6.79 × 0.7
=$4.75
Hope that was helpful.Thank you!!!
Please answer this question I give brainliest thank you! Number 8
Answer:
The third options
Step-by-step explanation:
Counting we can see that 10 students went to two or less states, and 10 went to three or more
The average height of students at UH from an SRS of 12 students gave a standard deviation of 2.5 feet. Construct a 95% confidence interval for the standard deviation of the height of students at UH. Assume normality for the data.a. (1.271, 6.245)b. (0.771, 10.245)c. (1.771, 4.245)d. (7.771, 9.245)e. (4.771, 10.245)f. None of the above
Answer:
c. [1.771;4.245] feet
Step-by-step explanation:
Hello!
The variable of interest is
X: height of a student at UH
X~N(μ;σ²)
You have to estimate the population standard deviation using a 95% confidence interval.
The statistic to use for the interval is a student Chi-Square with n-1 degrees of freedom. First you have to calculate the CI for the population variance:
[tex][\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}} ;\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}} ][/tex]
[tex]X^2_{n-1;1-\alpha /2}= X^2_{11;0.975}= 21.920[/tex]
[tex]X^2_{n-1;\alpha /2}= X^2_{11;0.025}= 3.816[/tex]
n=12
S= 2.5
[tex][\frac{11*6.25}{21.920} ;\frac{11*6.25}{3.816}} ][/tex]
[3.136; 18.016] feet²
Then you calculate the square root of both limits to get the CI for the population standard deviation:
[√3.136; √18.016]
[1.771;4.245] feet
I hope this helps!
A research organization keeps track of what citizens think is the most important problem facing the country today. They randomly sampled a number of people in 2003 and again in 2009 using a different random sample of people in 2009 than in 2003 and asked them to choose the most important problem facing the country today from the following choices, war, economy, health care, or other. Which of the following is the correct test to use to determine if the distribution of "problem facing this countrytoday" is different between the two different years?
A.
Use a chi-square test of homogeneity.
B.
Use a paired t-test.
C.
Use a two-sample z-test for proportions.
D.
Use a chi-square goodness-of-fit test.
Answer:
Step-by-step explanation:
From the information given, the population is divided into sub groups. Each group would consist of citizens picking a particular choice as the most important problem facing the country. The choices are the different categories. In this case, the null hypothesis would state that the distribution of proportions for all categories is the same in each population. The alternative hypothesis would state that the distributions is different. Therefore, the correct test to use to determine if the distribution of "problem facing this country today" is different between the two different years is
A) Use a chi-square test of homogeneity.
Nicola runs a small pottery cafe. Customers choose from a range of ceramics which they paint and personalise.
Nicola wants to make as much profit as possible on the sale of ceramic plates. She pays £1.28 for each plate. What is the most profit Nicola can make on one plate.
Answer:
Bb
Step-by-step explanation:
You are dealt one card from a 52 card deck. Then the card is replaced in the deck, the deck is shuffled, and you draw again. Find the probability of getting a picture card the first time and a club the second time. Express the probability as a simplified fraction. Group of answer choices
Answer:
3/52
Step-by-step explanation:
The picture card are j,q k and there are 4 of each so there are 12 picture cards
P( picture card) = picture card/ total
12/52 = 3/13
Then replace the card
There are 13 clubs
P( club) = club/ total
13/52 = 1/4
P(picture,replace,club) = 3/13*1/4 = 3/52
Consider random samples selected from the population of all female college soccer players in the United States. Assume the mean height of female college soccer players in the United States is 66 inches and the standard deviation is 3.5 inches. Which do you expect to have less variability (spread): a sampling distribution with sample size n
Answer:
Option C is correct.
The sampling distribution with sample size n=100 will have less variability.
Step-by-step explanation:
Complete Question
Consider random samples selected from the population of all female college soccer players in the United States. Assume the mean height of female college soccer players in the United States is 66 inches and the standard deviation is 3.5 inches. Which do you expect to have less variability (spread): a sampling distribution with sample size n = 100 or a sample size of n = 20.
A. Both sampling distributions will have the same variability.
B.The sampling distribution with sample size n=20 will have less variability
C. The sampling distribution with sample size n =100 will have less variability
Solution
The central limit theorem allows us to say that as long as
- the sample is randomly selected from the population distribution with each variable independent of each other and with the sample having an adequate enough sample size.
- the random sample is normal or almost normal which is guaranteed if the population distribution that the random sample was extracted from is normal or approximately normal,
1) The mean of sampling distribution (μₓ) is approximately equal to the population mean (μ)
μₓ = μ = 66 inches
2) The standard deviation of the sampling distribution or the standard error of the sample mean is related to the population standard deviation through
σₓ = (σ/√N)
where σ = population standard deviation = 3.5 inches
N = Sample size
And the measure of variability for a sampling distribution is the magnitude of the standard deviation of the sampling distribution.
For sampling distribution with sample size n = 100
σₓ = (3.5/√100) = 0.35 inch
For sampling distribution with sample size n = 20
σₓ = (3.5/√20) = 0.7826 inch
The standard deviation of the sampling distribution with sample size n = 20 is more than double that of the sampling distribution with sample size n = 100, hence, it is evident that the bigger the sample size, the lesser the standard deviation of the sampling distribution and the lesser the variability that the sampling distribution shows.
Hope this Helps!!!
HELP ASAP GIVING BRANLIST!!
Answer:
Question 1: 3 - 5 hours.
Question 2: 0 - 1 hour
Step-by-step explanation:
Question 1: As you can see in the diagram, the guy is moving really slowly and is almost stuck, therefore, it is 3 - 5 hours.
Question 2: In hours 0 - 1, you can see that the graph is the closest to vertical as it gets.
Arc CD is Two-thirds of the circumference of a circle. What is the radian measure of the central angle? StartFraction 2 pi Over 3 EndFraction radians StartFraction 3 pi Over 4 EndFraction radians StartFraction 4 pi Over 3 EndFraction radians StartFraction 3 pi Over 2 EndFraction radians CAN YOU SHOW WORK PLEASE
Answer:
[tex]\theta = \frac{4\pi}{3}[/tex]
Step-by-step explanation:
Given
Let A represent the Length of Arc CD and C, represents the circumference
[tex]A = \frac{2}{3} C[/tex]
Required
Find the central angle (in radians)
The length of arc CD in radians is as follows;
[tex]A = r\theta[/tex]
Where r is the radius and [tex]\theta[/tex] is the measure of central angle
The circumference of a circle is calculated as thus;
[tex]C = 2\pi r[/tex]
From the question, it was stated that the arc length is 2-3rd of the circumference;
This means that
[tex]A = \frac{2}{3} C[/tex]
Substitute [tex]2\pi r[/tex] for C and [tex]r\theta[/tex] for A
[tex]A = \frac{2}{3} C[/tex] becomes
[tex]r\theta = \frac{2}{3} * 2\pi r[/tex]
[tex]r\theta = \frac{4\pi r}{3}[/tex]
Divide both sides by r
[tex]\frac{r\theta}{r} = \frac{4\pi r}{3}/r[/tex]
[tex]\frac{r\theta}{r} = \frac{4\pi r}{3} * \frac{1}{r}[/tex]
[tex]\theta = \frac{4\pi r}{3} * \frac{1}{r}[/tex]
[tex]\theta = \frac{4\pi}{3}[/tex]
Hence, the measure of the central angle; [tex]\theta = \frac{4\pi}{3}[/tex]
Answer:
The answer is C on Edge 2020
Step-by-step explanation:
I did the assignment
Expand (2 + a)9 using Pascal’s triangle.
Answer:
Step-by-step explanation:
The Pascal triangle is used to determine the coefficients of the terms when we expand the expression.
1 [tex](A + B) ^ 0[/tex] = 1
1 1 [tex](A +B ) ^ 1 = 1A + 1B[/tex]
1 2 1 [tex](A+ B) ^ 2 = 1A^2 + 2 AB + 1B^2[/tex]
By extending the triangle, you will get the 9th row, which is your expression, of the coefficients. that is
1 9 36 84 126 126 84 36 9 1
Now, fill in AB in the gaps.
1AB + 9 AB + 36AB + 84AB + 126AB + 126AB +84AB + 36AB + 9AB + 1AB
Next, you need to go from the left to fill out the exponent of A and it will go down from 9 (the exponent of the whole thing) . That is
[tex]1A^9B+9A^8B+36A^7B+84A^6B+126A^5B+126A^4B+84A^3B+36A^2B+9A^1B+1A^0B[/tex]
Next will be the exponent of B. this time, you go from the right and do the same with A. You can go from the left also, but go up from 0 to 9 for the exponent of B
[tex]1A^9B^0+9A^8B^1+36A^7B^2+84A^6B^3+126A^5B^4+126A^4B^5+84A^3B^6+36A^2B^7+9A^1B^8+1A^0B^9[/tex]
The last step is just to simplify the A^0=1 and B^0 =1 at the first and the last terms.
[tex]A^9+9A^8B^1+36A^7B^2+84A^6B^3+126A^5B^4+126A^4B^5+84A^3B^6+36A^2B^7+9A^1B^8+B^9[/tex]
Hope you can learn the method
Solve the equation and express each solution in a+bi form x^4-7x^2-8=0
Answer:
x = ±2√2, ±i
Step-by-step explanation:
Step 1: Factor
(x² - 8)(x² + 1)
Step 2: Find roots
x² - 8 = 0
x² = 8
x = ±2√2
x² + 1 = 0
x² = -1
x = ±i
Answer:
The answer is B
Step-by-step explanation:
The assembly time for a product is uniformly distributed between 8 and 12 minutes.The mean and the variance of the assembly time are: a.4 minutes and 16 (minute)2 b.8 minutes and 12 (minute)2 c.12 minutes and 1.33 (minute)2 d.10 minutes and 1.33 (minute)2
Answer:
d. 10 minutes and 1.33 minutes.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The mean of the uniform distribution is:
[tex]M = \frac{a + b}{2}[/tex]
The variance of the uniform distribution is given by:
[tex]V = \frac{(b-a)^{2}}{12}[/tex]
The assembly time for a product is uniformly distributed between 8 and 12 minutes.
This means that [tex]a = 8, b = 12[/tex].
Mean:
[tex]M = \frac{8 + 12}{2} = 10[/tex]
Variance:
[tex]V = \frac{(12-8)^{2}}{12} = 1.33[/tex]
So the correct answer is:
d. 10 minutes and 1.33 minutes.
I need help with this
Answer:
Volume = 14.5 cm³
Step-by-step explanation:
Volume of cone = [tex]\pi r^2\frac{h}{3}[/tex]
Where r = 2 and h = 3.46
Volume = [tex](3.14)(2)^2\frac{3.46}{3}[/tex]
Volume = (3.14)(4)(1.15)
Volume = 14.5 cm³
Please answer this correctly
NEED GEOMETRY HELP ASAP (12 POINTS)
Answer:
HJ > PK
Step-by-step explanation:
Notice that the side PL in one triangle has the same length as side GJ in the other, and side GH has the same size as side LK of the other triangle. Now what is different is the angle subtended between these sides in the case of the triangle on the lower left, the subtended angle is [tex]90^o[/tex] , which is larger angle than that subtended between equal sides on the other triangle ([tex]85^o[/tex])
Therefore, if the angle subtended by the equivalent sides in the triangle on the left is larger than the angle subtended on the right hand side triangle, then the sides associated with such angle aperture must keep the inequality. That is:
Since [tex]\angle\,G\,\,\,>\,\,\,\angle \,L[/tex], then HJ > PK
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time. (a) Find the probability that at least 2 flights arrive late.
Answer:
83.29% probability that at least 2 flights arrive late.
Step-by-step explanation:
For each flight, there are only two possible outcomes. Either it arrives late, or it does not arrive late. The probability of a flight arriving late is independent of other flights. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
80 % of its flights arriving on time.
So 100 - 80 = 20% arrive late, which means that [tex]p = 0.2[/tex]
15 Southwest flights
This means that [tex]n = 15[/tex]
Find the probability that at least 2 flights arrive late.
Either less than two arrive late, or at least 2 do. The sum of the probabilities of these outcomes is 1. So
[tex]P(X < 2) + P(X \geq 2) = 1[/tex]
We want [tex]P(X \geq 2)[/tex]
Then
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{15,0}.(0.2)^{0}.(0.8)^{15} = 0.0352[/tex]
[tex]P(X = 1) = C_{15,1}.(0.2)^{1}.(0.8)^{14} = 0.1319[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0352 + 0.1319 = 0.1671[/tex]
Then
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.1671 = 0.8329[/tex]
83.29% probability that at least 2 flights arrive late.
Antipsychotic drugs are widely prescribed for conditions such as schizophrenia and bipolar disease. An article reported on body composition and metabolic changes for individuals who had taken various antipsychotic drugs for short periods of time. (a) The sample of 41 individuals who had taken aripiprazole had a mean change in total cholesterol (mg/dL) of 3.55, and the estimated standard error sD n was 3.478. Calculate a confidence interval with confidence level approximately 95% for the true average increase in total cholesterol under these circumstances. (Round your answers to two decimal places.)
Answer:
95% for the true average increase in total cholesterol under these circumstances
(-2.306 , 9.406)
Step-by-step explanation:
Step(i):-
Given sample size 'n' =41
Mean of the sample(x⁻) = 3.55
The estimated standard error
[tex]S.E = \frac{S.D}{\sqrt{n} }[/tex]
Given estimated standard error ( S.E) = 3.478
Level of significance ∝=0.05
Step(ii):-
95% for the true average increase in total cholesterol under these circumstances
[tex](x^{-} - t_{0.05} S.E ,x^{-} + t_{0.05} S.E)[/tex]
Degrees of freedom
ν= n-1 = 41-1 =40
t₀.₀₅ = 1.6839
95% for the true average increase in total cholesterol under these circumstances
[tex](x^{-} - t_{0.05} S.E ,x^{-} + t_{0.05} S.E)[/tex]
( 3.55 - 1.6839 ×3.478 ,3.55 + 1.6839 ×3.478 )
(3.55 - 5.856 , 3.55 + 5.856)
(-2.306 , 9.406)
Conclusion:-
95% for the true average increase in total cholesterol under these circumstances
(-2.306 , 9.406)