Answer:
a) True
Step-by-step explanation:
Repeated samples are a type of samples that are used to determine the features or characteristics or a given set of data.
In repeated samples, statistical techniques are applied whereby two samples that have similar characteristics are tested or analysed under different conditions.
Repeated samples can also be called matched or paired samples.
In repeated samples , we have what we refer to as confidence intervals. These are intervals whereby the true and correct value of certain parameters such as mean, the standard deviation of a given data or distribution is determined. We have confidence interval levels of 90%, 95% and 99%.
In repeated samples, approximately 99% of all differences in sample means will fall within the bounds of the interval already computed.
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?
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.
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.
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.
What is the common difference in the following arithmetic sequence?
7,3,-1,-5
Answer:
-4
Step-by-step explanation:
Each term is 4 less than the term before it, so the common difference is -4.
Answer:
B. -4 on edge !!
Step-by-step explanation:
Got it right :)
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
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
Which expression(s) have a greatest common factor (GCF) of 3xy2 with 42xy4
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.
Reina is buying a house either with brick or with siding, with 1 floor or with 2 floors, and in the city, the suburbs, or the
country. On top of that she can choose from 6 different interior paints and 9 different exterior paints.
Using the fundamental counting principle, simplify the expression
combinations
to determine the number of possible
There are possible combinations.
Reina decides she definitely wants a brick house with one floor. Now the number of possible combinations is
Answer:
1. There are 648 total combinations that can be chosen.
2. After she choses two possiblilities the total number changes to 108 total posibilities to chose from
Step-by-step explanation:
possibility: 1/2 x 1/3 x 1/2 x 1/6 x 1/9 = 648
then you remove the first two because she chose those ones
1/2 x 1/6 x 1/9 = 108 possibilities left
Answer:
Step-by-step explanation:
1. C
2. C
3. B
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}
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.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"†).
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.
What is the area of a triangle with a base of 7 cm and a height of 4cm
Answer:
14 sq cm
Step-by-step explanation:
7 × 4 = 28
28 ÷ 2 = 14
brainliest?
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%.
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.
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 ?
Answer:
24 324
Step-by-step explanation:
21334 fda adf
Answer: 24, 324
Step-by-step explanation:
Find the perimiter of both sides
Translate the English phrase into an algebraic expression, then evaluate the expression
Nine less than negative eighteen
Answer:-18-9=-17
Step-by-step explanation:
Answer:
-27
Step-by-step explanation:
Nine less than negative eighteen
[tex] - 18 - 9 = - 27[/tex]
here are the ingredients needed to make 8 pancakes
250ml milk
1 egg
140 g flour
5 g butter
a) simon makes 4 pancakes
workout how much milk he needs
b) craig makes 12 pancakes
workout how much butter he needs
To calculate milk needed for a different number of pancakes and determine the amount of butter for a varied pancake quantity.
To calculate the amount of milk needed for 4 pancakes that Simon is making:
Divide the amount of milk needed for 8 pancakes (250ml) by 2 since 4 is half of 8. 250ml ÷ 2 = 125ml.
To determine the amount of butter for the 12 pancakes that Craig is making:
Since the recipe calls for 5g of butter for 8 pancakes, we can calculate the amount needed for 12 pancakes by setting up a proportion: (5g/8 pancakes) = (x/12 pancakes). Solving for x gives x = 7.5g.
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)
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
#SPJ3
Solve for x. Write both solutions, separated
by a comma.
5x2 + 2x - 7 = 0
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
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.
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:
Which solids can have vertical cross sections that are circles? Check all that apply
-cones
-cylinders
-spheres
cones
cylinders
spheres
Step-by-step explanation:
The question was worded incorrectly and instead of giving the options it gave you the answers
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?
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.
solve this system using a systems of equations. Discount Rental Cars charges a daily fee plus a mileage fee for renting its cars. Barney was charge 145.00 for 3 days and 310 miles, while Mary was charge 250.00 for 5 days and 600 miles. What does discount Rental Cars charge per day and mile?
Answer:
Barney 145 3 Days 310 Miles
Mary 250 5 Days 600 Miles
A) 3 D + 310 M = 145
B) 5 D + 600 M = 250
Multiplying A) by -5/3
A) -5 D - 516.6666M = -241.66666666
B) 5D + 600M = 250
Adding A) and B)
83.3333 M = 8.3333333333
M = .10 per mile
3 D = 114
Daily Rate = 38 dollars per day
Step-by-step explanation:
An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 270 cars, they found a mean MPG of 27.8. Assume the variance is known to be 6.25. A level of significance of 0.02 will be used. Make a decision to reject or fail to reject the null hypothesis. Make a decision.
Answer:
The calculated value z = 1.3145 < 2.326 at 0.02 level of significance
The null hypothesis is accepted
Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.
Step-by-step explanation:
Step(i):-
An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.
The mean of the Population 'μ' = 28.0miles/gallon
Given data after testing 270 cars, they found a mean MPG of 27.8. Assume the variance is known to be 6.25.
The sample size 'n' = 270
Mean of the sample 'x⁻' = 27.8
Given Population variance 'σ² = 6.25
The standard deviation of Population 'σ' = √6.25 = 2.5
Step(ii):-
Null hypothesis :H₀: 'μ' = 28.
Alternative hypothesis :H₁: 'μ' ≠28.
The test statistic
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{27.8-28 }{\frac{2.5}{\sqrt{270} } } = \frac{-0.2}{0.15214}[/tex]
Z = -1.3145
|Z| = |-1.3145|= 1.3145
Step(iii):-
The tabulated value of z-score at 0.02 level of significance = 2.326
The calculated value z = 1.3145 < 2.326 at a t 0.02 level of significance
The null hypothesis is accepted
Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.
3x+5=3 solve this equation
Answer:
-3/2
Step-by-step explanation:
Answer: x = -2/3 = -0.667
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?
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.
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.
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.
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.
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.
A major home improvement store conducted its biggest brand recognition campaign in the company's history. A series of new television advertisements featuring well-known entertainers and sports figures were launched. A key metric for the success of television advertisements is the proportion of viewers who "like the ads a lot". A study of 1,189 adults who viewed the ads reported that 230 indicated that they "like the ads a lot." The percentage of a typical television advertisement receiving the "like the ads a lot" score is believed to be 22%. Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad (i.e.. if there is evidence that the population proportion of "like the ads a lot" for the company's ads is less than 0.22) at a 0.01 level of significance. Referring to the above, the null hypothesis will be rejected if the test statistic is:
The null hypothesis will be rejected if the test statistic is: greater than -2.33
The null hypothesis will be rejected if the test statistic falls within the critical region, which is determined by the significance level (0.01 in this case).
To determine the test statistic, calculate the z-score for the sample proportion and compare it to the critical value.
The formula to calculate the z-score for the sample proportion is:
[tex]z = (\hat{p} - p) / \sqrt(p * (1 - p) / n)[/tex]
Where:
[tex]\hat{p}[/tex] is the sample proportion (230/1189 = 0.193)
p is the population proportion (0.22)
n is the sample size (1189)
Calculating the z-score:
z = (0.193 - 0.22) / [tex]\sqrt[/tex](0.22 * (1 - 0.22) / 1189)
z = -2.25
To determine if the null hypothesis is rejected or not, compare the absolute value of the z-score to the critical value for a one-tailed test at a 0.01 significance level.
The critical value for a one-tailed test at a 0.01 significance level is approximately -2.33.
If the absolute value of the calculated z-score is greater than 2.33, we reject the null hypothesis.
Since absolute value of the calculated z-score is not greater than 2.33, null hypothesis is not rejected.
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.
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%.
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?
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.
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.
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
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
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
What is the median number of pairs of shoes owned by the children ?
Answer:
3
Step-by-step explanation: