For a random sample of 10 phone batteries produced using a new technol- ogy, the sample mean for the run time under a given load is 20.2 hours. The sample standard deviation of the battery run time is 0.6 hours. Calculate a 95% confidence 3 interval for the average run time. In addition, calculate the 99% lower and upper confidence bounds. State any assumptions that you make. (b) (5 marks) 100 random samples of water from a fresh water lake were taken and the calcium concentration (milligrams per liter) measured. A 95% CI on the mean calcium concentration is (0.49, 0.82]. Calculate a 99% CI on the mean calcium concentration. State any assumptions that you make. (c) (5 marks) A random sample of 2,000 circuits is collected and 56 are found to be defective. Calculate an approximate 99% confidence interval for the defect rate.
Answers
(a) 95% confidence interval for average run time: (19.832, 20.568), 99% confidence interval: (19.7044, 20.6956). Assumptions: random and representative sample, normal distribution, accurate estimate of population standard deviation.
(b) 99% confidence interval for mean calcium concentration: (0.458, 0.852). Assumptions: random and representative sample, normal distribution, estimated sample standard deviation as an accurate estimate of population standard deviation.
(c) Approximate 99% confidence interval for defect rate: (0.025, 0.047).
We have,
(a) To calculate a 95% confidence interval for the average run time of phone batteries, we can use the following formula:
Confidence interval = sample mean ± (critical value x (sample standard deviation / sqrt(sample size)))
Assuming a normal distribution and using a 95% confidence level, the critical value for a two-tailed test is approximately 1.96.
Substituting the given values into the formula:
Sample mean = 20.2 hours
Sample standard deviation = 0.6 hours
Sample size = 10
Confidence interval = 20.2 ± (1.96 x (0.6 / √(10)))
Confidence interval = 20.2 ± (1.96 x (0.6 / √(10)))
Confidence interval = 20.2 ± 0.368
Therefore, the 95% confidence interval for the average run time is (19.832, 20.568).
To calculate the 99% lower and upper confidence bounds, we can use the same formula with a different critical value.
Assuming a 99% confidence level, the critical value for a two-tailed test is approximately 2.58.
Confidence interval = 20.2 ± (2.58 x (0.6 / √(10)))
Confidence interval = 20.2 ± 0.4956
Therefore, the 99% confidence interval for the average run time is (19.7044, 20.6956).
Assumptions: The assumptions made here are that the sample is random and representative of the population, the run times of phone batteries are normally distributed, and the sample standard deviation is an accurate estimate of the population standard deviation.
(b) To calculate a 99% confidence interval on the mean calcium concentration, we can use the given confidence interval as a starting point.
Given: 95% CI = (0.49, 0.82]
To calculate the 99% confidence interval, we need to find the margin of error. Since we don't have the sample standard deviation, we can estimate it based on the range of 95% CI.
Estimated sample standard deviation = (upper bound - lower bound) / (2 x critical value)
Estimated sample standard deviation = (0.82 - 0.49) / (2 x 1.96) = 0.166
Using the estimated sample standard deviation, we can calculate the margin of error:
Margin of error = critical value x (sample standard deviation / sqrt(sample size))
Assuming the sample size is large enough, we can use the same critical value for the 99% CI as we used for the 95% CI (approximately 1.96).
Margin of error = 1.96 x (0.166 / √(100))
Margin of error = 0.032
To calculate the 99% CI, we adjust the lower and upper bounds of the 95% CI by adding and subtracting the margin of error:
99% CI = (lower bound - margin of error, upper bound + margin of error)
99% CI = (0.49 - 0.032, 0.82 + 0.032)
Therefore, the 99% confidence interval on the mean calcium concentration is (0.458, 0.852).
Assumptions: The assumptions made here are that the 100 random samples are representative of the population, the calcium concentrations are normally distributed, and the estimated sample standard deviation is an accurate estimate of the population standard deviation.
(c) To calculate an approximate 99% confidence interval for the defect rate, we can use the formula for a confidence interval on a proportion.
Confidence interval = sample proportion
Thus,
(a) 95% confidence interval for average run time: (19.832, 20.568), 99% confidence interval: (19.7044, 20.6956). Assumptions: random and representative sample, normal distribution, accurate estimate of population standard deviation.
(b) 99% confidence interval for mean calcium concentration: (0.458, 0.852). Assumptions: random and representative sample, normal distribution, estimated sample standard deviation as an accurate estimate of population standard deviation.
(c) Approximate 99% confidence interval for defect rate: (0.025, 0.047).
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Related Questions
Explain the slope and the y-intercept
Answers
Assume that the demand curve D(p) given below is the market demand for widgets:
Q=D(p)=3097−23pQ=D(p)=3097-23p, p > 0
Let the market supply of widgets be given by:
Q=S(p)=−5+10pQ=S(p)=-5+10p, p > 0
where p is the price and Q is the quantity. The functions D(p) and S(p) give the number of widgets demanded and supplied at a given price.
What is the equilibrium price?
Please round your answer to the nearest hundredth.
What is the equilibrium quantity?
Please round your answer to the nearest integer.
What is the price elasticity of demand (include negative sign if negative)?
Please round your answer to the nearest hundredth.
What is the price elasticity of supply?
Please round your answer to the nearest hundredth.
Answers
To find the equilibrium price and quantity in the given market, we need to determine the point where the quantity demanded (Qd) equals the quantity supplied (Qs).
We start by setting D(p) equal to S(p) and solving for the equilibrium price.
D(p) = S(p)
3097 - 23p = -5 + 10p
Combining like terms and isolating the variable, we get:
33p = 3102
p = 3102/33 ≈ 94.00
Therefore, the equilibrium price is approximately $94.00.
To find the equilibrium quantity, we substitute the equilibrium price into either the demand or supply equation. Let's use the demand equation:
Qd = 3097 - 23p
Qd = 3097 - 23(94)
Qd ≈ 853
Hence, the equilibrium quantity is approximately 853 widgets.
To calculate the price elasticity of demand, we use the formula:
PED = (ΔQd / Qd) / (Δp / p)
Substituting the equilibrium values, we have:
PED = (0 / 853) / (0 / 94)
PED = 0
The price elasticity of demand is 0 (zero), indicating perfect inelasticity, meaning that a change in price does not affect the quantity demanded.
For the price elasticity of supply, we use the formula:
PES = (ΔQs / Qs) / (Δp / p)
Substituting the equilibrium values, we have:
PES = (0 / 853) / (0 / 94)
PES = 0
The price elasticity of supply is also 0 (zero), indicating perfect inelasticity, meaning that a change in price does not affect the quantity supplied.
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assume you are asked to create a model that predicts the number of new babies born per period according to the size of the stork population. in this case, the number of babies is multiple choice an outcome. a feature. an observation. a target.
Answers
The number of babies in this problem is classified as an:
Target variable.Outcome.How to classify the variables?For each student, we have an input variable and an output variable, given as follows:
Input variable: Observation.Outcome variable: Target variable or outcome.For this problem, we have that the number of babies is predicted according to the size of the stork population, hence the variables are given as follows:
Input variable: Size of stork population.Outcome variable: Number of babies.This means that the number of babies can be classified as either the target variable or the outcome, as it is the output of the study, and then either the first and the last options are correct.
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jeff will pick a card at random from ten cards numbered 1 through 10. the number on this card will indicate his starting point on the number line shown below. he will then spin the fair spinner shown below (which has three congruent sectors) and follow the instruction indicated by his spin. from this new point he will spin the spinner again and follow the resulting instruction. what is the probability that he ends up at a multiple of 3 on the number line? express your answer as a common fraction.
Answers
Answer:
my
Step-by-step explanation:
namajeff
Compare these two number and use < or > to answer the question. 4.98
4.89
Answers
Answer:
4.98 > 4.89
Step-by-step explanation:
4.98 - 4.89 = .09
.09 difference making the statement true 4.98 > 4.89
The distance between two lines measured along a perpendicular line to the line is always the same.
Answers
The distance between two lines measured along a perpendicular line to the line is always the same is called as equidistant .
Given :
The distance between two lines measured along a perpendicular line to the line is always the same.
What is Equidistant ?
Distances between two points from a common points are equal then it is called as equidistant .
Formulas :
Midpoint = ( x1 + x2 / 2 , y1 + y2 / 2 )
Distance = \(\sqrt{(x2 - x1 )^2 - (y2 - y1)^2 }\)
These are two main formulas are used to find whether equidistant or not.
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Using 2 step equations
4 ( 2y - 3 ) = 28
Answers
Answer:
y=5
Step-by-step explanation:
8y=28-12
8y=16
Y=16/2=8
Examine whether participants who received different lengths of treatment differed significantly in the number of relapses they experienced.
Treatment Length M SD
Short Length (1-4 weeks) 4.95 4.26
Moderate length (5-7 weeks) 5.00 3.88
Long length (8+ weeks) 6.16 3.73
ANOVA
Number of relapses
Sum of Squares df Mean Square F Sig.
Between Groups 22.981 2 11.491 .680 .509
Within Groups 1978.319 117 16.909
Total 2001.300 119
Answers
The ANOVA table demonstrates that there was no significant difference between the participants who received treatment for various lengths of time in the number of relapses they experienced. The F-value was 0.680, with a corresponding p-value of 0.509, indicating that the null hypothesis (the three groups are not significantly different from one another) should not be rejected.
In other words, the participants who received different lengths of treatment did not have a significantly different number of relapses. The study's statistical analysis yielded results that were insignificant (F(2,117) = 0.680, p > 0.05), indicating that the number of relapses did not differ significantly based on the length of treatment received by the participants.
The participants' M values were similar across all three treatment duration categories: short length (1-4 weeks) at 4.95, moderate length (5-7 weeks) at 5.00, and long length (8+ weeks) at 6.16, but the difference was insignificant.
The participants' SD values were also similar across all three categories of treatment duration.
The short duration of treatment had an SD of 4.26, the moderate duration of treatment had an SD of 3.88, and the long duration of treatment had an SD of 3.73.
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The money used in Jordan is called the dinar. The exchange rate is $3 to 2 dinars. Find how many dollars you would recieve if you exchanged 22 dinars
Answers
Answer:
He would have received $33 if he exchanged 22 dinars
Step-by-step explanation:
3(-6+8)=(3x-6)+(3x8)
Answers
Answer:
= 6
Step-by-step explanation:
= 3 (-6 + 8)
= (3 * -6) + (3 * 8)
= -18 + 24
= 6
Answer:
\(x = 12\)
the answer is attached to the picture
hope this helps you.
Brainliest plzz
A textbook store sold a combined total of 288 history and chemistry textbooks in a week. The number of chemistry textbooks sold was 72 less than the number of history textbooks sold. How many textbooks of each type were sold?
Answers
The number οf histοry bοοks is 180 that sοld in a week. The number οf chemistry textbοοks is 108 sοld in a week.
What is an equatiοn?There are many different ways tο define an equatiοn. The definitiοn οf an equatiοn in algebra is a mathematical declaratiοn that illustrates the equality οf twο mathematical expressiοns.
Given that the tοtal number οf bοοks that sοld in a week is 288.
The number οf chemistry textbοοks sοld was 72 less than the number οf histοry textbοοks sοld.
Assume that the number οf histοry textbοοks sοld was x.
The number οf chemistry textbοοks sοld was (x-72)
The tοtal number οf bοοks sοld was x + (x-72) = 2x - 72.
Accοrding tο the questiοn:
2x - 72 = 288
Add 72 frοm bοth sides:
2x - 72 + 72 = 288 + 72
2x = 360
Divide bοth sides by 2:
x = 360/2
x = 180
The number οf histοry textbοοks sοld was 180.
The number οf chemistry textbοοks sοld was (180-72) = 108.
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Kevin paid $88.45 for a new pair of clippers. This
amount includes a tax of 7%. The cost of the new
pair of clippers before tax is?
Answers
Nelson covered the first 20 miles in 2 1/2 hours, what was his average speed in miles per hour?
Answers
Answer:
Nelson's average speed was 8 miles per hour.
Step-by-step explanation:
To find Nelson's average speed, you need to divide the distance he traveled by the time it took him to travel that distance. In this case, Nelson traveled 20 miles in 2 1/2 hours, so his average speed was 20 miles / 2.5 hours = <<20/2.5=8>>8 miles per hour.
Answer:
8 miles per hour
Step-by-step explanation:
In order to find Nelson's average speed, we can set up a proportion. To solve for x, x being miles traveled in one hour.
\(\frac{20 miles}{2.5hours} =\frac{x miles }{1 hour}\)
x= 8
what is the value of f
Answers
Answer:
f = 22
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
140° is an exterior angle of the triangle, thus
4f + 1 + 51 = 140, that is
4f + 52 = 140 ( subtract 52 from both sides )
4f = 88 ( divide both sides by 4 )
f = 22
please help urgent
Use the formula A = P(1 + rt) to find the indicated quantity. P=$7996; r = 6%; t = 10 months; Find A. OA. $8475.76 OB. $8395.80 OC. $399.80 OD. $6663.33
Answers
Answer:
B) \(\$8395.80\)
Step-by-step explanation:
\(A=P(1+rt)\\A=7996(1+0.06\cdot\frac{10}{12})\\A=7996(1+0.05)\\A=7996(1.05)\\A=\$8395.80\)
This is all assuming that r=6% is an annual rate, making t=10/12 years
f(x) = x2. What is g(x)?
Answers
Answer:
B
Step-by-step explanation:
Graph shrinks, that means for every x value there is a higher y value. So coefficient of x is definitely more than 1. Try to substitute x = 1 to (9x)^2 and (3x)^2.
(3(1))^2 = 9
What is the domain of this function?
{x|x >0}
{x|x <8)
{x|0
{xlx < 0x8}
Answers
Answer:
x≥0, or x=[0,∞)
Step-by-step explanation:
Domain is values of x.
x≥0, or x=[0,∞)
What will happen to the slope of line P if the line is shifted so that the y-intercept increases and the x-intercept remains the same?
The slope will change from positive to negative
The slope will increase
The slope will change from negative to positive
The slope will decrease
Answers
Answer:
Step-by-step explanation:
⊕ The slope will increase
The mass of a package sent through the mail is 3 kilograms what is the mass of the package in grams? Plz halp GAHAAHAHHAH
Answers
Answer:
3000 grams
Step-by-step explanation:
convert 3 Kg to G
Dominic bought 4 pencils and 3 highlighters for $9.80. Zoe bought 3 pencils
and 5 highlighters for $10.65. If Micha buys 2 pencils and 2 highlighters,
how much will it cost?
Answers
If Dominic bought 4 pencils and 3 highlighters for $9.80. it will cost Micha $5.50 to buy 2 pencils and 2 highlighters.
What is the cost?Set up two equations based on the purchases made by Dominic and Zoe:
Equation 1: 4p + 3h = 9.80
Equation 2: 3p + 5h = 10.65
Multiplying Equation 1 by 3 and Equation 2 by 4
Equation 3: 12p + 9h = 29.40
Equation 4: 12p + 20h = 42.60
Subtracting Equation 3 from Equation 4
(12p + 20h) - (12p + 9h) = 42.60 - 29.40
11h = 13.20
h = 13.20 / 11
h = 1.20
Substituting the value of h back into Equation 1
4p + 3(1.20) = 9.80
4p + 3.60 = 9.80
4p = 9.80 - 3.60
4p = 6.20
p = 6.20 / 4
p = 1.55
So,
Cost:
Cost = (2 * p) + (2 * h)
= (2 * $1.55) + (2 * $1.20)
= $3.10 + $2.40
= $5.50
Therefore it will cost Micha $5.50 to buy 2 pencils and 2 highlighters.
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7. LX -(3z +4z) - (6z - 2)
Answers
Answer: LX - 13z - 2
Step-by-step explanation:
(3z + 4z)= 7z
LX - 7z - (6z - 2)
LX + -7z + -6z + -2
LX + -13z + -2
= LX - 13z - 2
A radio transmission tower is 160 feet tall. How long should a guy wire be if it is to be attached 13 feet from the top and is to make an angle of 29\deg with the ground? Give your answer to the nearest tenth of a foot.
Answers
x = 147 / 0.5446 ≈ 270.2 ft
To find the length of the guy wire for a radio transmission tower, trigonometry concepts are applied. Given a tower height of 160 feet, with the wire attached 13 feet from the top and making an angle of 29° with the ground, we can solve for the length of the guy wire, represented by x.
Using the Pythagorean theorem and considering the right triangle formed by the tower height, the wire attachment point, and the ground, we can set up the equation:
x = √((160 - 13)² + x²)
Next, we apply the tangent function to the given angle:
tan(29°) = (160 - 13) / x
Simplifying, we have:
0.5446 = 147 / x
To solve for x, we rearrange the equation:
x = 147 / 0.5446 ≈ 270.2 ft
Rounding to the nearest tenth of a foot, the length of the guy wire required is approximately 270.2 feet. This wire is attached 13 feet from the top of the tower and makes a 29° angle with the ground.
Trigonometry plays a crucial role in solving real-world problems involving angles and distances. It provides a mathematical framework for calculating unknown values based on known information, enabling accurate measurements and constructions.
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help what is the awnswer of 6x - 2y = 14
Answers
Answer:
x=7+y/3
Step-by-step explanation:
Question 8 c
A bag of tokens contains 7 red, 9 green, and 6 blue tokens. What is the probability that
a randomly selected token is not red? Enter your answer as a fraction.
Answers
15/22 is the probability you won’t draw a red
n football gambling, when you bet an nfl tease and get an additional 6 points how often does that cover?
Answers
The most typical teaser in sports betting is a 6-point football teaser, which requires you to correctly predict the results of two games while also receiving six extra points on each spread.
It will pay about -120 depending on the book. Some bookies pay roughly 6-1 for a two-team, six-point pleaser. In order to break even, bettors must win each leg around 38% of the time.
Make sure your 6-point, two-team teasers pay -120 or greater. If you're not being treated fairly there, you most likely won't be on other teasers either.
If you're betting a 6-point teaser at -120, you need to win each leg 74% of the time to break even.
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HELP ASAPPPPPPPPPPPPP
Answers
Answer:
Answer: A
Step-by-step explanation:
(go to attachment to see explanation)
hope this helped :D
Consider using a z test to test
H0: p = 0.4.
Determine the P-value in each of the following situations. (Round your answers to four decimal places.)
a) Ha : p > 0.4, z= 1.49
Answers
The P-value for a one-tailed z-test with Ha: p > 0.4 and z = 1.49 is 0.0675, indicating insufficient evidence to reject the null hypothesis at the 0.05 level of significance.
How to find P-value for any situation?To find the P-value for a z-test with Ha: p > 0.4 and z = 1.49, we first calculate the corresponding area under the standard normal distribution curve.
Using a standard normal table or a calculator, we find that the area to the right of z = 1.49 is 0.0675.
Since the alternative hypothesis is one-tailed, the P-value is equal to the area in the tail to the right of z = 1.49.
Therefore, the P-value for this test is 0.0675 or 6.75% (rounded to four decimal places).
This means that if the null hypothesis is true, there is a 6.75% chance of observing a sample proportion as extreme as or more extreme than the one we obtained.
Since the P-value (6.75%) is greater than the significance level (α), we fail to reject the null hypothesis at the α = 0.05 level of significance. We do not have sufficient
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A regression model for a consumption function shows how household consumption and GDP have historically been related. The numbers in brackets underneath are the standard errors of the regression model. The coefficient in front of GDP is called the marginal propensity to consume, or MPC, because it is how much consumption goes up when GDP goes up by one unit. C-205 + 0.7 GDP (18) (0.051) A researcher finds that the marginal propensity to consume changes if she adds the % change in a stock market index as a variable. C-193+ 0.65 GDP+ 0.08 (% change in stock price) (14) (0.12) (0.01) What is predicted consumption if GDP is 200 and if the share market falls by 20%? (you do not have to worry about any effects of multicollinearity) 393 193. 321.4 322.98
Answers
Therefore, the predicted consumption, when GDP is 200 and the share market falls by 20%, is approximately -64.6.
To calculate the predicted consumption, we can use the regression equation:
C = -193 + 0.65 * GDP + 0.08 * (% change in stock price)
Given that GDP is 200 and the share market falls by 20% (which corresponds to a -20% change in stock price), we can substitute these values into the equation:
C = -193 + 0.65 * 200 + 0.08 * (-20)
C = -193 + 130 + (-1.6)
C = -193 + 130 - 1.6
C ≈ -64.6
Therefore, the predicted consumption, when GDP is 200 and the share market falls by 20%, is approximately -64.6.
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z=
Please help!!!!!!!
Answers
Answer:
37
Step-by-step explanation: sorry if wrong just trying to help
Simon and his track team ran on the Heron Peak running trail yesterday after school. The team ran 2 miles due west from the parking lot to a bench. They turned at the bench to run 1.5 miles due north toward an outhouse. To finish the run, the team ran a straight line from the outhouse back to the parking lot. If Simon ran at a constant rate of 8 miles per hour, how long did it take Simon to finish the run?
If necessary, round your answer to the nearest tenth.
how many minutes?
Answers
It took Simon 45 minutes to finish the run.
What is distance?
Distance is the measure of how far apart two objects or locations are from each other. It is usually measured in units such as meters, kilometers, miles, or feet.
To solve this problem, we need to use the distance formula:
Distance = Rate x Time
We can break down the run into three parts: the 2 miles due west, the 1.5 miles due north, and the straight line back to the parking lot.
For the first part, Simon ran 2 miles at a rate of 8 miles per hour. Therefore, the time it took him to run this part of the trail was:
Time = Distance / Rate
Time = 2 miles / 8 miles per hour
Time = 0.25 hours
For the second part, Simon ran 1.5 miles at a rate of 8 miles per hour. Therefore, the time it took him to run this part of the trail was:
Time = Distance / Rate
Time = 1.5 miles / 8 miles per hour
Time = 0.1875 hours
To find the distance of the last part, we need to use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the 2-mile and 1.5-mile legs:
c² = a² + b²
c² = 2² + 1.5²
c² = 4 + 2.25
c² = 6.25
c = sqrt(6.25)
c = 2.5 miles
So, Simon ran 2.5 miles at a rate of 8 miles per hour. Therefore, the time it took him to run this part of the trail was:
Time = Distance / Rate
Time = 2.5 miles / 8 miles per hour
Time = 0.3125 hours
Finally, we can add up the times for each part of the trail to find the total time it took Simon to finish the run:
Total Time = 0.25 hours + 0.1875 hours + 0.3125 hours
Total Time = 0.75 hours
To convert this to minutes, we can multiply by 60:
Total Time = 0.75 hours x 60 minutes/hour
Total Time = 45 minutes
Therefore, it took Simon 45 minutes to finish the run.
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