Answer:
Standard error for the proportion of social media users who are concerned about privacy
S.E = 0.0219
Step-by-step explanation:
Explanation:-
Given data recent survey of 500 social media users, 300 stated that they were concerned about privacy
Size of random sample 'n' = 500
x = 300
sample proportion [tex]p = \frac{x}{n} = \frac{300}{500} = 0.6[/tex]
Standard error for the proportion of social media users who are concerned about privacy is determined by
[tex]S.E = \sqrt{\frac{p(1-p)}{n} }[/tex]
[tex]S.E = \sqrt{\frac{0.6(1-0.6)}{500} }= 0.0219[/tex]
Does this sample have a bias
A concerned citizen
stands outside of the
courthouse with a petition to
outlaw tickets being given for
parking meters to be
removed.
Answer:
Yes, the sample has a bias
Step-by-step explanation:
Bias is the term used in statistics to describe a systematic distortion in the samples obtained for the parameter being estimated. It is evident by obtaining values higher or lower than that of the average population for the parameter being measured. As such the data is a misrepresentation of the population and cannot be trusted to give a good indices of things.
This sample has a bias because the concerned citizen opted to use a convenience sampling instead of using random sampling. In random sampling, every individual has an equal chance of being chosen which is unlike the convenience sampling when only a specific group of individuals can be chosen. In this case, the bias was introduced when the citizen went to stand outside the courthouse with his petition, the citizen should have taken samples across diverse geographical locations and professional institutions. The implication of this sampling is that a significant percentage of the population has been sidelined (considering they would not be in or around the courthouse) from the sampling and the sampling has been restricted to only those who have business around the courthouse. The result is that whatever samples he/she obtains will not be an accurate representation of the parameter being measure from the population.
As such, the sampling technique is biased
The waiting time for a train has a uniform distribution between 0 and 10 minutes. What is the probability that the waiting time for this train is more than 4 minutes on a given day? Answer: (Round to two decimal place.)
Answer:
0.6 = 60% probability that the waiting time for this train is more than 4 minutes on a given day
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X higher than x is given by the following formula.
[tex]P(X > x) = \frac{b - x}{b-a}[/tex]
The waiting time for a train has a uniform distribution between 0 and 10 minutes.
This means that [tex]a = 0, b = 10[/tex]
What is the probability that the waiting time for this train is more than 4 minutes on a given day?
[tex]P(X > x) = \frac{b - x}{b-a}[/tex]
[tex]P(X > 4) = \frac{10 - 4}{10 - 0} = 0.6[/tex]
0.6 = 60% probability that the waiting time for this train is more than 4 minutes on a given day
Which answer shows 2.13786 times 10 Superscript 4 written in standard form?
Answer:
Answer:
21378.6
Step-by-step explanation:
You move the decimal point four places towards the right.
Answer:
21378.6
Step-by-step explanation:
An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous records, 30% of all those making reservations do not appear for the trip. Answer the following questions, assuming independence wherever appropriate. (Round your answers to three decimal places.)
(a) If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip?
(b) If six reservations are made, what is the expected number of available places when the limousine departs?
Answer:
(a) The probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.
(b) The expected number of available places when the limousine departs is 0.338.
Step-by-step explanation:
Let the random variable Y represent the number of passenger reserving the trip shows up.
The probability of the random variable Y is, p = 0.70.
The success in this case an be defined as the number of passengers who show up for the trip.
The random variable Y follows a Binomial distribution with probability of success as 0.70.
(a)
It is provided that n = 6 reservations are made.
Compute the probability that at least one individual with a reservation cannot be accommodated on the trip as follows:
P (At least one individual cannot be accommodated) = P (X = 5) + P (X = 6)
[tex]={6 \choose 5}\ (0.70)^{5}\ (1-0.70)^{6-5}+{6 \choose 6}\ (0.70)^{6}\ (1-0.70)^{6-6}\\\\=0.302526+0.117649\\\\=0.420175\\\\\approx 0.4202[/tex]
Thus, the probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.
(b)
The formula to compute the expected value is:
[tex]E(Y) = \sum X\cdot P(X)[/tex]
[tex]P (X=0)={6 \choose 0}\ (0.70)^{0}\ (1-0.70)^{6-0}=0.000729\\\\P (X=1)={6 \choose 1}\ (0.70)^{1}\ (1-0.70)^{6-1}=0.010206\\\\P (X=2)={6 \choose 2}\ (0.70)^{2}\ (1-0.70)^{6-2}=0.059535\\\\P (X=3)={6 \choose 3}\ (0.70)^{3}\ (1-0.70)^{6-3}=0.18522\\\\P (X=4)={6 \choose 4}\ (0.70)^{4}\ (1-0.70)^{6-4}=0.324135[/tex]
Compute the expected number of available places when the limousine departs as follows:
[tex]E(Y) = \sum X\cdot P(X)[/tex]
[tex]=(4\cdot 0.000729)+(3\cdot 0.010206)+(2\cdot 0.059535)+(1\cdot 0.18522)\\+(0\cdot 0.324135)\\\\=0.002916+0.030618+0.11907+0.18522+0\\\\=0.337824\\\\\approx 0.338[/tex]
Thus, the expected number of available places when the limousine departs is 0.338.
How do you solve this problem
Answer: Undefined
Step-by-step explanation:
For this problem, we know that 3ˣ=-9. All we have to do is figure out what x is.
We know that any integer raised to the power cannot be negative. The closest answer we can get is x=2 because 3²=9. Unfortunately, we are looking for -9. Therefore, this x is undefined.
"National survey released in 2003 showed that among U.S. adults ages 70 and older, 21.1% had been told by a doctor that they had some form of cancer. Use this result as valid for the population of U.S. adults, 70 yrs. old and older. What is the probability that among 40 adults (ages 70 and older) chosen at random more than 22 percent will have been told by their doctor that they have cancer
Answer:
44.43% probability that among 40 adults (ages 70 and older) chosen at random more than 22 percent will have been told by their doctor that they have cancer
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question, we have that:
[tex]p = 0.211, n = 40[/tex]
So
[tex]\mu = 0.211, s = \sqrt{\frac{0.211*0.789}{40}} = 0.0645[/tex]
What is the probability that among 40 adults (ages 70 and older) chosen at random more than 22 percent will have been told by their doctor that they have cancer
This is 1 subtracted by the pvalue of Z when X = 22. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.22 - 0.211}{0.0645}[/tex]
[tex]Z = 0.14[/tex]
[tex]Z = 0.14[/tex] has a pvalue of 0.5557
1 - 0.5557 = 0.4443
44.43% probability that among 40 adults (ages 70 and older) chosen at random more than 22 percent will have been told by their doctor that they have cancer
An economist is studying the job market in Denver area neighborhoods. Let x represent the total number of jobs in a given neighborhood, and let y represent the number of entry-level jobs in the same neighborhood. A sample of six Denver neighborhoods gave the following information (units in hundreds of jobs).x 15 32 51 28 50 25y 3 3 7 5 9 3Complete parts (a) through (e), given Σx = 201, Σy = 30, Σx2 = 7759, Σy2 = 182, Σxy = 1163, and r ≈ 0.872.a. Draw a scatter diagram displaying the data.b. Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r.c. Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)d. Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.
Answer:
The sample correlation coefficient is, r = 0.8722.
The equation of the least-squares line is:
[tex]y= -0.161+0.154x[/tex]
Step-by-step explanation:
(a)
The scatter diagram displaying the data for X : total number of jobs in a given neighborhood and Y : number of entry-level jobs in the same neighborhood is shown below.
(b)
The table attached below verifies the values of [tex]\sum X,\ \sum Y,\ \sum X^{2},\ \sum Y^{2}\ \text{and}\ \sum XY[/tex].
The sample correlation coefficient is:
[tex]\begin{aligned}r~&=~\frac{n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}} {\sqrt{\left[n \sum{X^2}-\left(\sum{X}\right)^2\right] \cdot \left[n \sum{Y^2}-\left(\sum{Y}\right)^2\right]}} \\r~&=~\frac{ 6 \cdot 1163 - 201 \cdot 30 } {\sqrt{\left[ 6 \cdot 7759 - 201^2 \right] \cdot \left[ 6 \cdot 182 - 30^2 \right] }} \approx 0.8722\end{aligned}[/tex]
Thus, the sample correlation coefficient is, r = 0.8722.
(c)
The slope and intercept are:
[tex]\begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 30 \cdot 7759 - 201 \cdot 1163}{ 6 \cdot 7759 - 201^2} \approx -0.161 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 6 \cdot 1163 - 201 \cdot 30 }{ 6 \cdot 7759 - \left( 201 \right)^2} \approx 0.154\end{aligned}[/tex]
The equation of the least-squares line is:
[tex]y= -0.161+0.154x[/tex]
(d)
The least-squares line is graphed in the diagram below.
A special deck of cards has ten cards. Four are green, three are blue, and three are red. When a card is picked, its color of it is recorded. An experiment consists of first picking a card and then tossing a coin.
a. List the sample space.
b. Let A be the event that a blue card is picked first, followed by landing a head on the coin toss. Find P(A).
c. Let B be the event that a red or green is picked, followed by landing a head on the coin toss. Are the events A and B mutually exclusive? Explain your answer in one to three complete sentences, including numerical justification.
d. Let C be the event that a red or blue is picked, followed by landing a head on the coin toss. Are the events A and C mutually exclusive? Explain your answer in one to three complete sentences, including numerical justification.
Answer:
(a) S = {GH, GT, BH, BT, RH and RT}
(b) The value of P (A) is 0.15.
(c) A and B mutually exclusive.
(d) A and C are not mutually exclusive.
Step-by-step explanation:
There are 10 cards in a special deck of cards: 4 are green (G), 3 are blue (B), and 3 are red (R).
Also when a card is picked, its color of it is recorded. An experiment consists of first picking a card and then tossing a coin.
(a)
The sample space is:
S = {GH, GT, BH, BT, RH and RT}
(b)
A = a blue card is picked first, followed by landing a head on the coin toss
Compute the probability of event A as follows:
[tex]P(A)=P(B)\times P(H)[/tex]
[tex]=\frac{3}{10}\times\frac{1}{2}\\\\=\frac{3}{20}\\\\=0.15[/tex]
Thus, the value of P (A) is 0.15.
(c)
B = a red or green is picked, followed by landing a head on the coin toss.
The result of the coin toss is same for both events A and B.
So, consider the events,
A as a blue card is picked first
B as a red or green is picked
There is no intersection point for the two events.
Thus, events A and B mutually exclusive.
(d)
C = a red or blue is picked, followed by landing a head on the coin toss.
The result of the coin toss is same for both events A and C.
So, consider the events,
A as a blue card is picked first
C as a red or blue is picked
There is an intersection point for the two events.
Thus, events A and C are not mutually exclusive.
Part(a): The sample space can be written as shown below:
[tex]S=\{GH,GT,BH,BT,RH,RT\}[/tex]
Part(b): The required probability is [tex]P(A)=0.15[/tex]
Part(c): The events A and B are mutually exclusive because of [tex]P( A\ AND\ B ) = 0[/tex] are equal to zero.
Part(d): The events A and C are not mutually exclusive because [tex]P( A\ AND\ C ) = 0[/tex] are not equal to zero.
Samples Space:A sample space is a collection of a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”.
Part(a):
A special deck contains ten cards with colors red, green, and blue when the card is picked its color gets recorded, and after that coin will get tossed.
Then the sample space can be written as shown below:
[tex]S=\{GH,GT,BH,BT,RH,RT\}[/tex]
Part(b):
If A is the event that a blue card is picked first followed by landing ahead on the coin toss then the outcome it contains is 3 blue cards and 1 head.
Therefore the [tex]P(A)[/tex] is calculated below:
[tex]P(A):P(B)\timesP(H)\\=\frac{3}{10}\times\frac{1}{2}\\ =0.15[/tex]
Part(c):
Mutually exclusive events contain a probability [tex]P( A\ AND\ B ) = 0[/tex] that means there is no common outcome between them.
Here, it can be noticed that events A and B cannot happen at the same time. That means, the researcher cannot pick the same cards together. Either it could be red or green.
Hence, events A and B are mutually exclusive because of [tex]P( A\ AND\ B ) = 0[/tex] are equal to zero.
Part(d):
Mutually exclusive events contain a probability [tex]P( A\ AND\ C ) = 0[/tex] which means there is no common outcome between them.
Here, it can be noticed that events A and C can happen at the same time because event C can contain all outcomes of event A.
Hence, events A and C are not mutually exclusive because [tex]P( A\ AND\ C ) = 0[/tex] are not equal to zero.
Learn more about the topic samples space:
https://brainly.com/question/10684603
The following are the ages (years) of 5 people in a room: 12, 20, 22, 22, 23 A person enters the room. The mean age of the 6 people is now 23. What is the age of the person who entered the room?
Answer:
39
Step-by-step explanation:
12+20+22+22+23=99
new mean=23
23*6=138
138-99=39
eBookThe manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is or less. A member of the hotel's accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of future weekend guest bills to test the manager's claim.a. Which form of the hypotheses should be used to test the manager's claim
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is
The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel’s accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of
weekend guest bills to test the manager’s claim.
a. Which form of the hypotheses should be used to test the manager’s claim? Explain.
1) H0:μ ≥ 600
Ha:μ < 600
2) H0:μ ≤ 600
Ha:μ > 600
3) H0:μ=600
Ha:μ≠600
b. What conclusion is appropriate when H0 cannot be rejected?
c. What conclusion is appropriate when H0 can be rejected?
Solution:
a) the hypotheses should be used to test the manager’s claim is
H0:μ ≤ 600
Ha:μ > 600
This is because the already known or assumed mean guest bill for a weekend is 600 or less. This forms the null hypothesis. The alternative is the opposite of the null hypothesis. Since the alternative states that it is increasing, the sign,> would be used.
b) If H0 cannot be rejected, it means that there is no sufficient evidence to reject H0 at the given level of significance.
c) if H0 can be rejected, it means that there is sufficient evidence to reject H0 at the given level of significance.
Determine the total number of roots of each polynomial function. g(x) = 5x - 12x2 + 3
Answer:
2 total roots
x = -1/3, 3/4
Step-by-step explanation:
We can use the discriminant b² - 4ac to find how many roots a polynomial has.
Answer:
2Step-by-step explanation:
Edginuity 2021
PLEASE HELP***
solve for x
Answer:
x =8
Step-by-step explanation:
The angles are vertical angles which means they are equal
4x+112 = 9x+72
Subtract 4x from each side
112 = 5x+72
Subtract 72 from each side
40 = 5x
Divide each side by 5
40/5 =x
8 =x
Answer: [tex]x=8[/tex]
Step-by-step explanation: Because they are opposite angles, they can be assumed to be equal to each other. Therefore, you can set the two equations equal to each other, creating [tex]9x+72=4x+112[/tex], and from there you can subtract [tex]4x[/tex] as well as [tex]72[/tex] from both sides to get [tex]5x=40[/tex]. Then, divide both sides by [tex]5[/tex] to get [tex]x=8[/tex].
A child takes a bouquet of flowers and a group of small vases, and places a single flower in each vase, so
that no vases or flowers are left over. What mathematical relationship have they just established between
the bouquet of flowers and the group of vases?
Answer:
Step-by-step explanation:
this graph shows the outside temperature (in degrees celsius) over the course of 12 hours, starting at midnight (x=0)
Answer:
You can add graph by using the edit button and uploading a picture of the screen. if you then cut the picture before uploading so it just shows the graphand not the question. We cna then try answer for you.
Step-by-step explanation:
Generally graphs starting at point x=0 would show a different value for y by looking and counting up to its temperature.
if this shows positive it would be above the x axis line if it shows negative it would be a minus value below the x axis line under zero on y.
Therefore when we get to hr 2 and see this change you can count across and count up and see the rate of change is either 1,2,3,4,56,7,8 etc difference or 1x 2x 3x 4 x 5x 6 x as multiples.This then indicates a scale change at certain points.
answer part two please
Answer:
a.) 8x + 6y
b.) 4x + 2y
Step-by-step explanation:
Simply add like terms together (x with x and y with y).
Can someone explain to me? i don't understand it
Step-by-step explanation:
I will do 12 and 14 as examples.
12) Angles of a triangle add up to 180°.
m∠P + m∠Q + m∠R = 180
5x − 14 + x − 5 + 2x − 9 = 180
8x − 28 = 180
8x = 208
x = 26
m∠P = 5x − 14 = 116
m∠Q = x − 5 = 21
m∠R = 2x − 9 = 43
14) If two sides of a triangle are equal, then the angles opposite those sides are also equal.
(Conversely, if two angles are equal, then the sides opposite those angles are also equal. Such a triangle is called an isosceles triangle.)
BC ≅ BD, so m∠C = m∠D.
5x − 19 = 2x + 14
3x = 33
x = 11
m∠B = 13x − 35 = 108
m∠C = 5x − 19 = 36
m∠D = 2x + 14 = 36
I need help to solve this grid question
Answer:
20 x 20 grid = 1066.67 cm wire
Step-by-step explanation:
Using unitary method
9 grid = 24 cm wire
1 grid = [tex]\frac{24}{9}[/tex] cm wire
Multiplying both sides by 400 (20 x 20)
400 grid = [tex]\frac{24}{9} * 400[/tex] cm
20 x 20 grid = 1066.67 cm wire
Please answer this correctly
Answer:
the correct answer is
Step-by-step explanation:
So, the probability is:P(greater than 4)=26=13. This is a theoretical probability, which is the observed number of favorable outcomes out of a certain number of trials. For instance, suppose you rolled the six-sided die five times, and got the following results:2,6,4,5,6
hope this help you!!!!!
Answer:
1/5 chance.
Step-by-step explanation:
There is only one number, 5, that is greater than 4 and there are 5 total numbers so there is a 1/5 chance selecting that number.
You randomly select one card from a 52-card deck. Find the probability of selecting the four of spades or the ace of clubs.
(Type answer an integer or a fraction. Simplify your answer.)
Answer:
1/26
Step-by-step explanation:
There is 1 four of spades, and 1 ace of clubs.
So the probability is 2/52, or 1/26.
Answer:
P(four of spades or ace of clubs)= 1/26
Step-by-step explanation:
In a deck of 52 cards, there is one four of spaces and one ace of clubs. we want to find the probability of selecting those cards.
P(four of spades or ace of clubs)=four of spades+ace of clubs/total cards
There is 1 four of spades and 1 ace of clubs. 1+1=2
P(four of spades or ace of clubs)=2/total cards
There are 52 total cards in a deck.
P(four of spades or ace of clubs)=2/52
This fraction can be simplified. Both the numerator (top number) and denominator (bottom number) can be divided by 2.
P(four of spades or ace of clubs)= (2/2) / (52/2)
P(four of spades or ace of clubs)= 1/26
Divide up the number 480 in a ratio of 3:5.
Answer:
180:300
Step-by-step explanation:
You first divide 480 by 8 because 3+5= 8 and then you multiply that answer (60) by 3 to get 180 and then you multiply it by 5 to get 300. So you get the ratio of 180:300.
Make the appropriate conclusion. Choose the correct answer below. A. RejectReject H0. There is insufficientinsufficient evidence at the alphaαequals=0.100.10 level of significance to conclude that the true mean heart rate during laughter exceeds 7171 beats per minute. B. Do not rejectDo not reject H0. There is insufficientinsufficient evidence at the alphaαequals=0.100.10 level of significance to conclude that the true mean heart rate during laughter exceeds 7171 beats per minute. C. RejectReject H0. There is sufficientsufficient evidence at the alphaαequals=0.100.10 level of significance to conclude that the true mean heart rate during laughter exceeds 7171 beats per minute. D. Do not rejectDo not reject H0. There is sufficientsufficient evidence at the alphaαequals=0.100.10 level of significance to conclude that the true mean heart rate during laughter exceeds 7171 beats per minute.
Answer:
a) Option D is correct.
H0: μ = 71
Ha: μ > 71
b) Option F is correct
z > 1.28
c) z = 2.85
d) Option C is correct.
Reject H0.There is sufficient evidence at the α = 0.10 level of significance to conclude that the true mean heart rate during laughter exceeds 71 beats per minute.
Step-by-step explanation:
a) 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.
This question aims to test the the true mean heart rate during laughter exceeds 71 beats per minute.
Hence, the null hypothesis is that there isn't sufficient evidence to say that the true mean heart rate during laughter exceeds 71 beats per minute. That is, the true mean doesn't exceed 71 beats per minute.
And the alternative hypothesis is that there is sufficient evidence to say that the true mean heart rate during laughter exceeds 71 beats per minute.
Mathematically,
The null hypothesis is represented as
H₀: μ = 71
The alternative hypothesis is represented as
Hₐ: μ > 71
b) Using z-distribution, the rejection area is obtained from the confidence level at which the test is going to be performed. Since the hypothesis test tests only in one direction,
Significance level = (100% - confidence level)/2
0.10 = 10% = (100% - confidence level)/2
20% = 100% - (confidence level)
Confidence level = 100% - 20% = 80%
Critical value for 80% confidence level = 1.28
And since we are testing if the true mean heart rate during laughter exceeds 71 beats per minute, the rejection area would be
z > 1.28
c) The test statistic is given as
z = (x - μ)/σₓ
x = sample mean = 73.4
μ = 71
σₓ = standard error = (σ/√n)
σ = 8
n = Sample size = 90
σₓ = (8/√90) = 0.8433
z = (73.4 - 71) ÷ 0.8433
z = 2.846 = 2.85
d) Since the z-test statistic obtained, 2.85, is firmly in the rejection area, z > 1.28, we reject the null hypothesis, accept the alternative hypothesis and say that there is sufficient evidence at the α = 0.10 level of significance to conclude that the true mean heart rate during laughter exceeds 71 beats per minute.
Hope this Helps!!!
EXREAMLY URGENT!! WILL FOREVER THANK YOU!!!! PLS JUST TAKE A LOOK!!!!! 20. What is the area of triangle XWZ?
Answer:
72√3
Step-by-step explanation:
30 60 90 triangles are what you start out with.
Step 1: 30-60-90
x = 12
WZ = 12√3
Step 2: Area formula
A = 1/2(12)(12√3)
*Since the 2 30-60-90 triangles are congruent, both segments of the base are 12
Plug it into the calc and you should get A = 72√3 as your final answer!
please very soon I offer the crown !!! + 10 points urgently !!!
The graphs below have the same shape. What is the equation of the blue
graph?
Answer:
C. G(x)= x³ + 1
Step-by-step explanation:
The graph has moved to right by one point so the function is:
G(x)= x³ + 1
option C is correct
Suppose the Acme Drug Company develops a new drug, designed to prevent colds. The company states that the drug is equally effective for men and women. To test this claim, they choose a simple random sample of 100 women and 200 men from a population of 100,000 volunteers. At the end of the study, 38% of the women caught a cold; and 51% of the men caught a cold. Based on these findings, can we reject the company's claim that the drug is equally effective for men and women? Use a 0.05 level of significance.
a) Hypothesis: (In both symbols and words)
b) Decision rule:
c) Calculation:
d) Conclusion:
Answer:
a) Null hypothesis: the drug is equally effective for men and women (company's claim)
Alternative hypothesis: the drug effectiveness significantly differs for men and women.
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
b) If the P-value is smaller than the significance level, the null hypothesis is rejected. If not, the null hypothesis failed to be rejected.
c) In the explanation.
d) As the P-value (0.0342) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the drug effectiveness significantly differs for men and women.
The company's claim is rejected.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim of the company, will be stated in the null hypothesis. We will test if there is evidence against that claim to reject it or not.
Then, the test claim is that the drug effectiveness significantly differs for men and women.
The null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
The significance level is 0.05.
The sample 1 (women), of size n1=100 has a proportion of p1=0.38.
The sample 2 (men), of size n2=200 has a proportion of p2=0.51.
The difference between proportions is (p1-p2)=-0.13.
[tex]p_d=p_1-p_2=0.38-0.51=-0.13[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{38+102}{100+200}=\dfrac{140}{300}=0.467[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.467*0.533}{100}+\dfrac{0.467*0.533}{200}}\\\\\\s_{p1-p2}=\sqrt{0.002489+0.001244}=\sqrt{0.003733}=0.061[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.13-0}{0.061}=\dfrac{-0.13}{0.061}=-2.1276[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]P-value=2\cdot P(z<-2.1276)=0.0342[/tex]
As the P-value (0.0342) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the drug effectiveness significantly differs for men and women.
A direct variation function contains the points (-9, -3) and (-12,4). Which equation represents the function?
Answer:
[tex]y = -\frac{7x}{3} - 24[/tex]
Step-by-step explanation:
We can model this function using the equation of a line:
[tex]y = ax + b[/tex]
Where a is the slope of the line and b is the y-intercept.
To find the values of a and b, we can use the two points given:
(-9, -3):
[tex]-3 = a * (-9) + b[/tex]
[tex]-9a + b = -3[/tex]
(-12, 4):
[tex]4 = a * (-12) + b[/tex]
[tex]-12a + b = 4[/tex]
If we subtract the second equation from the first one, we have:
[tex]-12a + b - (-9a + b) = 4 - (-3)[/tex]
[tex]-12a + 9a = 4 + 3[/tex]
[tex]-3a = 7[/tex]
[tex]a = -7/3[/tex]
Then, finding the value of b, we have:
[tex]-12a + b = 4[/tex]
[tex]28 + b = 4[/tex]
[tex]b = -24[/tex]
So the equation is:
[tex]y = -\frac{7x}{3} - 24[/tex]
Simply -5+2(x-3)+7x :)
Answer:
9x-11
Step-by-step explanation:
-5+2(x-3)+7x
Distribute
-5 +2x -6 +7x
-11 +9x
9x-11
Answer:
[tex]= 9x - 11 \\ [/tex]
Step-by-step explanation:
[tex] - 5 + 2(x - 3) + 7x \\ - 5 + 2x - 6 + 7x \\ - 5 - 6 + 2x + 7x \\ - 11 + 9x \\ = 9x - 11[/tex]
Find the domain and range of the following function ƒ(x) = 5|x - 2| + 4 Domain: [4,8) Range: (-∞,∞) Domain: (4,∞) Range: (-∞,∞) Domain: (-∞,∞) Range: [4,∞) Domain: (-∞,∞) Range: (4,∞)
Answer:
Step-by-step explanation:
Hi,
the function is defined for all reals so the domain is [tex]]-\infty;+\infty[[/tex]
for x real
|x| >= 0
so f(x) >= 4
so the range is [tex][4;+\infty[[/tex]
do not hesitate if you need any further explanation
hope this helps
Answer:
Domain: (-∞,∞) Range: (4,∞)
Find f(2) if f(x) = (x + 1)2
Answer:
9
Step-by-step explanation:
f(x) = (x + 1)^2
Let x=2
f(2) = (2 + 1)^2
= 3^2
= 9
What position did Theodore Roosevelt hold before he became president?
Answer:
He served as Assistant Secretary of the Navy under President William McKinley
hope i helped
-lvr