3. Danielle wants to know if she is over paying her auto insurance compared to her colleagues. She sent out a survey to a randomly selected 50 colleagues through email, and 30 of them responded. Here is the summary of the responded data. Danielle is paying $476, please help Danielle to find out if she is over paying for her auto insurance. (No points will be given without necessary steps). Sample STD 75 Minimum 397 Maximum 447 663 (1) What are the sample and population of the study? (2) Conduct appropriate statistical inference to help Danielle to address her concerns. (3) Based on your inference, what type of error could occur? Explain the error using the context words.
Answers
Answer:
a) - The population consists of all of Danielle's colleagues that could have been one of the randomly surveyed 50.
- The sample is Danielle's 50 colleagues that she ramdomly sampled.
b) From the statistical test performed, there is significant evidence to conclude that Danielle is truly overpaying for her auto insurance compared to her colleagues.
c) Check Explanation
Step-by-step explanation:
The full complete, correct question is attached to the solution of this question.
a) The population is normally the extended distribution where every selected random sample is extracted from. So, for this question, the population will be all of Danielle's colleagues.
The sample is the subset distribution obtained from the population. In the question, it is stated explicitly that Danielle randomly picked 50 of her colleagues to participate in the survey. Hence, the sample is Danielle's 50 colleagues that she ramdomly sampled.
b) The appropriate statistical inference for this question is to carry out the t-test hypothesis test.
For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question, Danielle wants to prove that she is overpaying for her auto insurance compared to her colleagues.
So, the null hypothesis is that there is no significant evidence to conclude that Danielle is overpaying for her auto insurance compared to her colleagues.
That is, Danielle isn't overpaying for her auto insurance compared to her colleagues or better stated that her colleagues are paying more than or just about the same for auto insurance compared to her.
While, the alternative hypothesis is that there is significant evidence to conclude that Danielle is overpaying for her auto insurance compared to her colleagues.
Let μ be the mean Danielle's colleagues' auto insurance fees.
Mathematically,
The null hypothesis is represented as
H₀: μ ≥ 476
The alternative hypothesis is given as
Hₐ: μ < 476
To do this test, we will use the t-distribution because no information on the population standard deviation is known
So, we compute the t-test statistic
t = (x - μ₀)/σₓ
x = sample mean = $447
μ₀ = Danielle's auto insurance bill that we're comparing the sample against = $476
σₓ = standard error = [σ/√n]
σ = Sample standard deviation = $75
n = Sample size = 30 (30 colleagues got back to Danielle)
σₓ = [75/√30] = $13.693
t = (447 - 476) ÷ 13.693
t = -2.117 = -2.12
checking the tables for the p-value of this t-statistic
Degree of freedom = df = n - 1 = 30 - 1 = 29
Significance level = 0.05 (Most hypothesis tests are carried out at this level of significance)
The hypothesis test uses a one-tailed condition because we're testing only in one direction. (Checking whether Danielle is overpaying or that the mean is of her colleagues' auto insurance fees is less than Danielle's)
p-value (for t = -2.12, at 0.05 significance level, df = 29, with a one tailed condition) = 0.021342
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.05
p-value = 0.021342
0.021342 < 0.10
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that Danielle is truly overpaying for her auto insurance compared to her colleagues.
c) The two type of errors associated with this test include the Type I and Type II errors.
In Hypothesis testing, A type I error involves rejecting the null hypothesis and accepting the alternative hypothesis when in reality, the null hypothesis is true.
A type II error involves failing to reject the null hypothesis when in reality it should have been rejected. It entails not rejecting the null hypothesis and making conclusions based on the null hypothesis, when in reality, the alternative hypothesis should have been accepted together with its conclusion.
For this question, a type I error entails obtaining from the statistical test that Danielle is overpaying when she isn't overpaying for her auto insurance compared to her colleagues in reality.
A type II error would be obtaining from the statistical test that Danielle isn't overpaying when she is truly overpaying for her auto insurance compared to her colleagues, in reality.
Hope this Helps!!!
Related Questions
A random sample of 28 plastic items is obtained, and their breaking strengths are measured. The sample mean is 7.142 and the sample standard deviation is 0.672. Conduct a hypothesis test to assess whether there is evidence that the average breaking strength is not 7.000.
Answers
Answer:
The test statistic t = 1.126 < 1.703 of '27' degrees of freedom at 0.05 level of significance.
null hypothesis(H₀ ) is accepted
There is evidence that the average breaking strength is 7.000.
Step-by-step explanation:
Step 1:-
Given random sample size (n) =28 <30
small sample size n= 28
The sample mean (x⁻) = 7.142
sample standard deviation (S) =0.672
Step 2:-
Null hypothesis :- there is evidence that the average breaking strength is 7.000.
H₀ : μ =7
Alternative hypothesis:-there is evidence that the average breaking strength is 7.000.
H₁ : μ ≠7
The test statistic [tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
Substitute all values and simplification ,
[tex]t = \frac{7.142 -7}{\frac{0.672}{\sqrt{28} } } = \frac{0.142 }{0.1269}[/tex]
t = 1.126
Calculated value is t = 1.126
The degrees of freedom γ = n-1 = 28-1 =27
The tabulated value t= 1.703 at degrees of freedom at 0.05 level of significance.
since calculated t < tabulated value 't' value of 27 degrees of freedom at 0.05 level of significance.
null hypothesis(H₀ ) is accepted
There is evidence that the average breaking strength is 7.000.
Translate the English phrase into an algebraic expression, then evaluate the expression
Nine less than negative eighteen
Answers
Answer:-18-9=-17
Step-by-step explanation:
Answer:
-27
Step-by-step explanation:
Nine less than negative eighteen
[tex] - 18 - 9 = - 27[/tex]
A bag contains 3 white balls, 4 green balls, and 5 red balls. A ball is drawn at random. How many total number of outcomes are there?
Answers
Answer:
12.
Step-by-step explanation:
Given that,
Number of while balls are 3
Number of green balls are 4
Number of red balls are 5
We need to find the total number of outcomes. We know the total number of outcomes in is number of choices.
In this case, total number of outcomes are the sum of all color balls i.e. 3 + 4 + 5 = 12 balls.
Hence, the total number of outcomes are 12.
Final answer:
The total number of outcomes when one ball is drawn at random from a bag containing 3 white, 4 green, and 5 red balls is 12.
Explanation:
A bag contains 3 white balls, 4 green balls, and 5 red balls. The total number of possible outcomes when a ball is drawn at random is simply the sum of all the balls in the bag. Since each ball can be selected in one distinct way, we calculate the total number of outcomes by adding the number of white balls, the number of green balls, and the number of red balls.
So, the total number of outcomes is:
3 (white) + 4 (green) + 5 (red) = 12 (total outcomes)
Therefore, there are 12 different possible outcomes when one ball is drawn at random from this bag.
Let X denote the courtship time for a randomly selected female-male pair of mating scorpion flies (time from the beginning of interaction until mating). Suppose the mean value of X is 120 min and the standard deviation of X is 110 min (suggested by data in the article "Should I Stay or Should I Go? Condition- and Status-Dependent Courtship Decisions in the Scorpion Fly Panorpa Cognate"†).
Answers
The question is a college-level mathematics problem focusing on statistics related to normal distribution, particularly the calculation of probabilities, defining a random variable, and understanding hypothesis testing and p-values.
Explanation:The student's question pertains to the concept of normal distribution and statistics as applied to biological data. Specifically, it involves analysis using the mean and standard deviation of a dataset, and proper understanding of hypothesis testing and p-values in scientific research.
Understanding the Random Variable X
The random variable X, in this context, represents the duration of criminal trials. The question requires defining X and calculating related probabilities using the normal distribution properties. A probability statement and sketching of the graph would aid in visual understanding of the probabilities in question.
In statistical hypothesis testing, a p-value less than the level of significance (e.g., 0.01) typically leads to rejection of the null hypothesis, indicating evidence supporting the alternative hypothesis. The data on fruit flies' fecundity and genetic traits provided is an example of such an analysis.
In a certain region, 15% of people over the age of 50 didn’t graduate from high school. We would like to know if this percentage is the same among the 25-50 year age group. What is the minimum number of 25-50 year old people who must be surveyed in order to estimate the proportion of non-grads to within 6% of the true parameter with 99% confidence?
Answers
Answer:
235 people
Step-by-step explanation:
Given:
P' = 15% = 0.15
1 - P' = 1 - 0.15 = 0.85
At 99% confidence leve, Z will be:
[tex] \alpha [/tex] = 1 - 99%
= 1 - 0.99 = 0.01
[tex] \alpha /2 = \frac{0.01}{2} = 0.005 [/tex]
[tex] Z\alpha/2 = 0.005 [/tex]
Z0.005 = 2.576
For the minimum number of 25-50 year old people who must be surveyed in order to estimate the proportion of non-grads to within 6%, we have:
Margin of error, E = 6% = 0.06
sample size = n = [tex] (\frac{Z\alpha /2}{E})^2 * P* (1 - P) [/tex]
[tex] = (\frac{2.576}{0.06}) ^2 * 0.15 * 0.85 [/tex]
= 235.02 ≈ 235
A number of 235 people between 25-30 years should be surveyed .
Answer:
n = 236
Step-by-step explanation:
Solution:-
- The proportion of people over the age of 50 who didn't graduate from high school are, p = 0.15 - ( 15 % )
- We are to evaluate the minimum sample size " n " from the age group of 25-50 year in order to estimate the proportion of non-grads within a standard error E = 6% of the true proportion p within 99% confidence.
- The minimum required sample size " n " for the standard error " E " for the original proportion p relation is given below:
[tex]n = \frac{(Z_\alpha_/_2)^2 * p* ( 1 - p )}{E^2}[/tex]
- The critical value of standard normal is a function of significance level ( α ), evaluated as follows:
significance level ( α ) = ( 1 - CI/100 )
= ( 1 - 99/100 )
= 0.01
- The Z-critical value is defined as such:
P ( Z < Z-critical ) = α / 2
P ( Z < Z-critical ) = 0.01 / 2 = 0.005
Z-critical = Z_α/2 = 2.58
- Therefore the required sample size " n " is computed as follows:
[tex]n = \frac{(2.58)^2 * 0.15* ( 1 - 0.15 )}{0.06^2}\\\\n = \frac{6.6564 * 0.1275}{0.0036}\\\\n = \frac{0.848691}{0.0036}\\\\n = 235.7475\\[/tex]
Answer: The minimum sample size would be next whole number integer, n = 236.
A simple random sample of 120 vet clinics in the Midwest reveals that the vast majority of clinics only treat small pets (dogs, cats, rabbits, etc.) and not large animals (cows, horses, etc.). Of the 120 clinics sampled, 88 responded that they do not treat large animals at their clinic. If a 95% confidence interval were calculated instead of 90% confidence interval, what would happen to the width of the confidence interval?
Answers
Answer:
the interval would get bigger.
Step-by-step explanation:
if you wanted to be more confident in the interval you're giving, you would make more of the answers fit under the umbrella you're hypothetically creating.
Use a one-sample t ‑test, based on the data below, to test the null hypothesis H0:µ=100.63 against the alternative hypothesis H1:µ>100.63 . The sample has a mean of x⎯⎯⎯=101.09 and a standard deviation of s=0.4887 . 100.68,101.23,100.82,101.15,100.96,100.70,102.09 Calculate the standard error (SE) and the t ‑statistic for this test. Give the standard error to four decimal places and t to three decimal places.
Answers
Answer:
The standard error (SE) is 0.1847.
The t-statistic for this test is 2.490.
Step-by-step explanation:
We are given that the sample has a mean of [tex]\bar X[/tex] = 101.09 and a standard deviation of s = 0.4887 .
Also, the 7 sample values are also given.
Let [tex]\mu[/tex] = population mean.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 100.63
Alternate Hypothesis, [tex]H_1[/tex] : [tex]\mu[/tex] > 100.63
The test statistics that would be used here One-sample t test statistics as we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean = 101.09
s = sample standard deviation = 0.4887
n = sample values = 7
The Standard Error (SE) is given by = [tex]\frac{s}{\sqrt{n} }[/tex] = [tex]\frac{0.4887}{\sqrt{7} }[/tex] = 0.1847
So, test statistics = [tex]\frac{101.09-100.63}{\frac{0.4887}{\sqrt{7} } }[/tex] ~ [tex]t_6[/tex]
= 2.490
The value of t test statistics is 2.490.
An Individual Retirement Account (IRA) has $17 comma 000in it, and the owner decides not to add any more money to the account other than interest earned at 4%compounded daily. How much will be in the account 30years from now when the owner reaches retirement age?
Answers
Answer: The owner reaches at Rs. 56438.28 after 30 years.
Step-by-step explanation:
Since we have given that
Sum = Rs. 17000
Rate of compounded daily = 4%
Number of years = 30 years
So, Using "compound interest formula" we get that :
[tex]A=P(1+\dfrac{r}{n})^{nt}\\\\A=17000(1+\dfrac{0.04}{365})^{365\times 30}\\\\A=17000(1.000109589)^{10950}\\\\A=56438.28[/tex]
Hence, The owner reaches at Rs. 56438.28 after 30 years.
Question 3
4 pts
(03.05)
What does 7 >-2 indicate about the positions of 7 and -2 on the number line? (4 points)
0
7 is located on the right of -2, and -2 is located on the right of o
0
7 is located on the left of -2, and -2 is located on the right of o
04
7 is located to the right of -2
7 is located on the left of -2
Question 4
4 pts
Answers
Answer:
7 is located to the right of -2
Step-by-step explanation:
Larger numbers are to the right on a number line, so the statement that 7 is larger than -2 means ...
7 is located to the right of -2
Suppose that $2n$ tennis players compete in a round-robin tournament. Every player has exactly one match with every other player during $2n-1$ consecutive days. Every match has a winner and a loser. Show that it is possible to select a winning player each day without selecting the same player twice. \\ \\ \textit{Hint: Remember Hall's Theorem}
Answers
Answer:
Step-by-step explanation:
given that Suppose that $2n$ tennis players compete in a round-robin tournament. Every player has exactly one match with every other player during $2n-1$ consecutive days.
this is going to be proved by contradiction
Let there be a winning player each day where same players wins twice, let n = 3there are 6 tennis players and match occurs for 5daysfrom hall's theorem, let set n days where less than n players wining a day let on player be loser which loses every single day in n days so, players loose to n different players in n daysif he looses to n players then , n players are winnerbut, we stated less than n players are winners in n days which is contradiction.so,we can choose a winning players each day without selecting the same players twice.Braydon, a scuba diver, has a tank that holds 6 liters of air under a pressure of 220 pounds per square inch (psi).
Write the equation that relates pressure, P, to volume, V.
If the pressure increases to 330 psi, how much air is held in Braydon’s tank?
Answers
Answer: 4 litres of air is held in Braydon’s tank.
Step-by-step explanation:
The law relating pressure to volume is the Boyle's law. It states that the volume of a given mass of gas is inversely proportional to its pressure as long as temperature remains constant. It is expressed as
P1V1 = P2V2
Where
P1 and P2 are the initial and final pressures of the gas.
V1 and V2 are the initial and final volumes of the gas.
From the information given,
V1 = 6 litres
P = 220 psi
P2 = 330 psi
Therefore,
6 × 220 = 330V2
V2 = 1320/330 = 4 litres
Answer:
V=1320/p
the tank holds 4 liters
Step-by-step explanation:
An experiment is carried out 400 times the possible outcomes are void fail and success if the frequency of void is 96 and the relative frequency is 0.24 then how much is the frequency of fail and success
Answers
the frequency of success is 244.
part b's answer is 240.
A relative frequency distribution shows the proportion of the total number of observations associated with each value or class of values and is related to a probability distribution, which is extensively used in statistics.
Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario. The relative frequency formula is given as:
Relative Frequency = Subgroup frequency/ Total frequency.
1. Frequency of success
=400 - 96 - 60
=244
relative frequency of fail
=60/400= 0.15
Relative Frequency of success
=1-0.15 - 0.24
=0.61
Learn more about relative frequency here:
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3x+5=3 solve this equation
Answers
Answer:
-3/2
Step-by-step explanation:
Answer: x = -2/3 = -0.667
what is 81,007-26,318?
Answers
Answer:
54689
Step-by-step explanation:
Callie evaluated the expression 0.42 times 4.73 using the steps shown below. 0.42 times 4.73 = 1.26. 1.26 + 29.40 + 168.00 = 198.66 Which best explains Callie’s error? Callie incorrectly placed the decimal. Callie multiplied incorrectly. Callie added incorrectly. Callie incorrectly used placeholder zeros.
Answers
Answer:
The correct option is;
Callie multiplied incorrectly
Step-by-step explanation:
Here we have 0.42 × 4.73 = 1.9866 then
1.9866 + 29.4 + 168 = 199.3866
Therefore, from the question, we had 0.42 × 4.73 = 1.26 which is incorrect, meaning that Callie multiplied incorrectly
Apparently, Callie multiplied as follows;
0.42 × 3 = 1.26 but what was in the question was
0.42 × 4.73 which is equal to 1.9866.
Answer:
Callie multiplied incorrectly
Step-by-step explanation:
all the credit goes to guy above me
Solve for x. Write both solutions, separated
by a comma.
5x2 + 2x - 7 = 0
Answers
Answer:
it equals 1
Step-by-step explanation:
(5)(2)+2x−7=5
Step 1: Simplify both sides of the equation.
(5)(2)+2x−7=5
10+2x+−7=5
(2x)+(10+−7)=5(Combine Like Terms)
2x+3=5
2x+3=5
Step 2: Subtract 3 from both sides.
2x+3−3=5−3
2x=2
Step 3: Divide both sides by 2.
2x
2
=
2
2
x=1
Which solids can have vertical cross sections that are circles? Check all that apply
-cones
-cylinders
-spheres
Answers
cones
cylinders
spheres
Step-by-step explanation:
The question was worded incorrectly and instead of giving the options it gave you the answers
What is the area of a triangle with a base of 7 cm and a height of 4cm
Answers
Answer:
14 sq cm
Step-by-step explanation:
7 × 4 = 28
28 ÷ 2 = 14
brainliest?
A certain university has 8 vehicles available for use by faculty and staff. Six of these are vans and 2 are cars. On a particular day, only two requests for vehicles have been made. Suppose that the two vehicles to be assigned are chosen at random from the 8 vehicles available. (Enter your answers as fractions.)
a.) Let E denote the event that the first vehicle assigned is a van. What is P(E) ?
b.) Let F denote the probability that the second vehicle assigned is a van. What is P(F|E)?
c.) Use the results of parts(a) and (b) to calculate P(E and F)
Answers
Answer:
a) [tex]P(E) = \frac{6}{8}[/tex]
b) [tex]P(F|E) = \frac{5}{7}[/tex]
c) [tex]P(E \cap F) = \frac{15}{28}[/tex]
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
We have that:
8 vehicles, of which 6 are vans.
a.) Let E denote the event that the first vehicle assigned is a van. What is P(E) ?
8 vehicles, of which 6 are vans.
So
[tex]P(E) = \frac{6}{8}[/tex]
b.) Let F denote the probability that the second vehicle assigned is a van. What is P(F|E)?
P(F|E) is the probability that the second vehicle assigned is a van, given that the first one was.
In this case, there are 7 vehicles, of which 5 are vans. So
[tex]P(F|E) = \frac{5}{7}[/tex]
c.) Use the results of parts(a) and (b) to calculate P(E and F)
[tex]P(F|E) = \frac{P(E \cap F)}{P(E)}[/tex]
[tex]P(E \cap F) = P(F|E)P(E)[/tex]
[tex]P(E \cap F) = \frac{6}{8}\frac{5}{7}[/tex]
[tex]P(E \cap F) = \frac{15}{28}[/tex]
The probability of the first vehicle assigned being a van is 3/4, and the conditional probability of the second vehicle being a van given the first was a van is 5/7. The probability that both vehicles assigned are vans is 15/28.
Explanation:The subject of this question is probability, a topic in Mathematics. We are asked to find the probability of a certain event occurring under certain conditions.
P(E), the probability that the first vehicle assigned is a van. Since there are 6 vans out of 8 vehicles, the probability is 6/8 or 3/4.P(F|E), the conditional probability that the second vehicle assigned is a van given that the first vehicle assigned was a van. After the first van has been assigned, there are now 5 vans left out of 7 vehicles. Therefore, the probability is 5/7.Finally, to find P(E and F), which is the probability that both vehicles assigned are vans, we multiply the probabilities we found in parts (a) and (b), so (3/4) * (5/7) = 15/28.Learn more about Probability here:https://brainly.com/question/22962752
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rectangle 2 is a scale drawing of rectangle b and has 25% of its area if rectangle A has side lengths of 4cm and 5cm what are the side lengths of rectangle b ?
Answers
Answer:
24 324
Step-by-step explanation:
21334 fda adf
Answer: 24, 324
Step-by-step explanation:
Find the perimiter of both sides
A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are C(x)equals72 comma 000 plus 70 x and p (x )equals 300 minus StartFraction x Over 20 EndFraction , 0less than or equalsxless than or equals6000. (A) Find the maximum revenue. (B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set. (C) If the government decides to tax the company $4 for each set it produces, how many sets should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for each set?
Answers
Answer:
Part (A)
1. Maximum revenue: $450,000Part (B)
2. Maximum protit: $192,5003. Production level: 2,300 television sets4. Price: $185 per television setPart (C)
5. Number of sets: 2,260 television sets.6. Maximum profit: $183,8007. Price: $187 per television set.Explanation:
0. Write the monthly cost and price-demand equations correctly:
Cost:
[tex]C(x)=72,000+70x[/tex]
Price-demand:
[tex]p(x)=300-\dfrac{x}{20}[/tex]
Domain:
[tex]0\leq x\leq 6000[/tex]
1. Part (A) Find the maximum revenue
Revenue = price × quantity
Revenue = R(x)
[tex]R(x)=\bigg(300-\dfrac{x}{20}\bigg)\cdot x[/tex]
Simplify
[tex]R(x)=300x-\dfrac{x^2}{20}[/tex]
A local maximum (or minimum) is reached when the first derivative, R'(x), equals 0.
[tex]R'(x)=300-\dfrac{x}{10}[/tex]
Solve for R'(x)=0
[tex]300-\dfrac{x}{10}=0[/tex]
[tex]3000-x=0\\\\x=3000[/tex]
Is this a maximum or a minimum? Since the coefficient of the quadratic term of R(x) is negative, it is a parabola that opens downward, meaning that its vertex is a maximum.
Hence, the maximum revenue is obtained when the production level is 3,000 units.
And it is calculated by subsituting x = 3,000 in the equation for R(x):
R(3,000) = 300(3,000) - (3000)² / 20 = $450,000Hence, the maximum revenue is $450,000
2. Part (B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set.
i) Profit(x) = Revenue(x) - Cost(x)
Profit (x) = R(x) - C(x)[tex]Profit(x)=300x-\dfrac{x^2}{20}-\big(72,000+70x\big)[/tex]
[tex]Profit(x)=230x-\dfrac{x^2}{20}-72,000\\\\\\Profit(x)=-\dfrac{x^2}{20}+230x-72,000[/tex]
ii) Find the first derivative and equal to 0 (it will be a maximum because the quadratic function is a parabola that opens downward)
Profit' (x) = -x/10 + 230 -x/10 + 230 = 0-x + 2,300 = 0x = 2,300Thus, the production level that will realize the maximum profit is 2,300 units.
iii) Find the maximum profit.
You must substitute x = 2,300 into the equation for the profit:
Profit(2,300) = - (2,300)²/20 + 230(2,300) - 72,000 = 192,500Hence, the maximum profit is $192,500
iv) Find the price the company should charge for each television set:
Use the price-demand equation:
p(x) = 300 - x/20p(2,300) = 300 - 2,300 / 20p(2,300) = 185Therefore, the company should charge a price os $185 for every television set.
3. Part (C) If the government decides to tax the company $4 for each set it produces, how many sets should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for each set?
i) Now you must subtract the $4 tax for each television set, this is 4x from the profit equation.
The new profit equation will be:
Profit(x) = -x² / 20 + 230x - 4x - 72,000Profit(x) = -x² / 20 + 226x - 72,000ii) Find the first derivative and make it equal to 0:
Profit'(x) = -x/10 + 226 = 0-x/10 + 226 = 0-x + 2,260 = 0x = 2,260Then, the new maximum profit is reached when the production level is 2,260 units.
iii) Find the maximum profit by substituting x = 2,260 into the profit equation:
Profit (2,260) = -(2,260)² / 20 + 226(2,260) - 72,000Profit (2,260) = 183,800Hence, the maximum profit, if the government decides to tax the company $4 for each set it produces would be $183,800
iv) Find the price the company should charge for each set.
Substitute the number of units, 2,260, into the equation for the price:
p(2,260) = 300 - 2,260/20p(2,260) = 187.That is, the company should charge $187 per television set.
What is the median number of pairs of shoes owned by the children ?
Answers
Answer:
3
Step-by-step explanation:
A golf ball is selected at random from a golf bag. If the golf bag contains 5 type A balls, 8 type B balls, and 3 type C balls, find the probability that the golf ball is not a type A ball.
Answers
Final answer:
The probability that a randomly selected golf ball from the bag is not a type A ball is 11/16, as we calculate this by dividing the number of non-type A balls (11) by the total number of balls (16).
Explanation:
The probability that the golf ball selected at random is not a type A ball can be found by first determining the total number of balls in the golf bag and then subtracting the number of type A balls to obtain the number of non-type A balls. The total number of balls is 5 type A balls + 8 type B balls + 3 type C balls = 16 balls. The number of non-type A balls is 8 type B balls + 3 type C balls = 11 balls.
To find the probability that the selected ball is not a type A ball, we divide the number of non-type A balls by the total number of balls, which gives us a probability of 11/16.
Final answer:
The probability that a randomly selected golf ball from the bag is not a type A ball is 0.6875 or 68.75%.
Explanation:
To find the probability that the golf ball selected at random is not a type A ball, we need to determine the total number of non-type A balls in the golf bag and divide it by the total number of balls in the bag. The golf bag contains 5 type A balls, 8 type B balls, and 3 type C balls, so the total number of balls in the bag is 5 + 8 + 3 = 16. There are 8 + 3 = 11 non-type A balls (type B and type C).
The probability of selecting a non-type A ball is then given by the number of non-type A balls divided by the total number of balls:
Probability = Number of non-type A balls / Total number of balls
We calculate it as:
Probability = 11 / 16 = 0.6875
Thus, the probability that the selected golf ball is not a type A ball is 0.6875 or 68.75%.
The director of a radio broadcasting company wants to determine whether the mean length of commercials on his station is equal to 24 seconds. He samples 200 commercials, and finds that the average length of these commercials is 26.3 seconds, with a standard deviation of 7.2 seconds. He uses a significance level of 5%. What is the value of the test statistic?
Answers
Answer:
The value of t test statistics is 4.518.
Step-by-step explanation:
We are given that director of a radio broadcasting company wants to determine whether the mean length of commercials on his station is equal to 24 seconds.
He samples 200 commercials, and finds that the average length of these commercials is 26.3 seconds, with a standard deviation of 7.2 seconds.
Let [tex]\mu[/tex] = mean length of commercials on his station.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 24 seconds {means that the mean length of commercials on his station is equal to 24 seconds}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 24 seconds {means that the mean length of commercials on his station is different from 24 seconds}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average length of these commercials = 26.3 seconds
s = sample standard deviation = 7.2 seconds
n = sample of commercials = 200
So, test statistics = [tex]\frac{26.3-24}{\frac{7.2}{\sqrt{200} } }[/tex] ~ [tex]t_1_9_9[/tex]
= 4.518
The value of t test statistics is 4.518.
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.1-in and a standard deviation of 1-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 4.3% or largest 4.3%.
Answers
Final answer:
The question involves Mathematics and requires understanding of statistics and normal distribution to find z-scores for designing helmets to fit a specific range of male head breadths, accommodating all except the smallest and largest 4.3%.
Explanation:
The subject of this question is Mathematics, specifically focusing on statistics and the concept of normal distribution. Engineers designing helmets need to consider the breadths of male heads, which are normally distributed with a given mean and standard deviation. The design requirements stipulate that the helmets should fit all men except for those in the extremities of the distribution (smallest 4.3% and largest 4.3%).
To address such a problem, one would typically use the z-score to identify the cutoff points on a standard normal distribution that correspond to these percentages. The z-score represents the number of standard deviations a data point is from the mean. Therefore, the engineers must calculate the z-scores that correspond to the smallest and largest 4.3% of the distribution to determine the range of head breadths the helmets must accommodate.
A 90% confidence interval for the mean height of students
is (60.128, 69.397). What is the value of the margin of error?
a) m = 129.525
b) m = 4.635
c) m = 64.763
d) m = 9.269
Answers
Answer:
[tex] ME= \frac{69.397-60.128}{2}= 4.6345 \approx 4.635[/tex]
And the best answer on this case would be:
b) m = 4.635
Step-by-step explanation:
Let X the random variable of interest and we know that the confidence interval for the population mean [tex]\mu[/tex] is given by this formula:
[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}} [/tex]
The confidence level on this case is 0.9 and the significance [tex]\alpha=1-0.9=0.1[/tex]
The confidence interval calculated on this case is [tex]60.128 \leq \mu \leq 69.397[/tex]
The margin of error for this confidence interval is given by:
[tex]ME =t_{\alpha/2} \frac{s}{\sqrt{n}} [/tex]
Since the confidence interval is symmetrical we can estimate the margin of error with the following formula:
[tex] ME = \frac{Upper -Lower}{2}[/tex]
Where Upper and Lower represent the bounds for the confidence interval calculated and replacing we got:
[tex] ME= \frac{69.397-60.128}{2}= 4.6345 \approx 4.635[/tex]
And the best answer on this case would be:
b) m = 4.635
The following stem-and-leaf plot represents the test scores for 22 students in a class on their most recent test. Use the data provided to find the quartiles.
Test Scores by Student
Stem Leaves
6 1 6 6 6
7 1 3 4
8 1 1 5 5 7 8 8 9
9 1 3 3 3 7 7 7
Key: 6||1=61
Step 1 of 3 : Find the second quartile.
Answers
Using the median concept, it is found that the second quartile is of 86.
What is the median of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile. The median is also called the second quartile, as [tex]\frac{2}{4} \times 100 = 50[/tex].
In this problem, there are 22 scores, which is an even number, hence the median is the mean of the 11th and the 12th scores.
From the stem-and-leaf plot, we have that:
The 1st score, in an increasing way, is 61.The 2nd, 3rd and 4th is 66.The 11th score is 85.The 12th score is 87.Then:
(85 + 87)/2 = 86
The second quartile is of 86.
You can learn more about the median concept at https://brainly.com/question/25215461
To find the quartiles of a dataset, arrange the data in ascending order, determine the median (Q2), split the data into a lower half and an upper half (excluding the median if the number of data points is odd), and find Q1 and Q3 as the medians of these subgroups.
Explanation:To find the quartiles for a set of test scores, first arrange the data from lowest to highest and then divide the dataset into four equal parts. The second quartile (Q2), also known as the median, separates the data into two halves. In this case, because we have 22 data points, the median will be the average of the 11th and 12th data points.
To calculate the first quartile (Q1), we find the median of the lower half of the data, which consists of the 10 scores below the overall median. Since we have an even number of data points in the lower half, Q1 will be the average of the 5th and 6th smallest scores.
Similarly, the third quartile (Q3) is the median of the upper half, consisting of the 10 scores above the overall median. Q3 will be the average of the 5th and 6th highest scores within this upper half.
Which expression(s) have a greatest common factor (GCF) of 3xy2 with 42xy4
Answers
Final answer:
None of the provided expressions have a greatest common factor of 3xy² with 42xy⁴ because they do not contain the necessary factors of 3, x, and y².
Explanation:
The student is asking for expressions that have a greatest common factor (GCF) of 3xy² with 42xy⁴. To find expressions with a GCF of 3xy², we need to look for expressions that include multiples of 3xy² in their factorization.
Looking at the provided expressions:
8ry (2x-1) does not have a GCF of 3xy² because it does not contain the necessary factors of 3 and y².3y similarly lacks x and has only y to the first power, not y².6(22-1) provided also does not contain the full factor of 3xy².4xp(y-2) has the x and p factors, but not 3y².The expression 3(4) simply equals 12, which is not a multiple of 3xy².None of the remaining provided expressions contain the necessary factors of 3xy² either.Therefore, none of the provided expressions have a GCF of 3xy² with 42xy⁴.
Meta-analysis involves:
a. averaging all the test statistics from every possible study on a given topic.
b. finding all studies published on a topic, calculating the effect size for each of those studies, and averaging the effect sizes together to find the average size of the effect across all studies.
c. finding all studies published on a topic, contacting the authors of the studies to request their original data, and then analyzing all the obtained data in one large analysis of variance.
d. attempting to recreate the experimental conditions of every published study on a given topic.
Answers
Answer: b. finding all studies published on a topic, calculating the effect size for each of those studies, and averaging the effect sizes together to find the average size of the effect across all studies.
Step-by-step explanation:
Based on these tables, what can you determine about the students in this class? Check all that apply.
There are 35 students in the class.
11 of the students are boys who have summer birthdays.
19 of the students are boys.
There is not enough information shown to determine how many girls have summer birthdays.
Answers
Answer:
Step-by-step explanation:
It’s 1 3,and 4
Answer:
1,3,4
Step-by-step explanation: