Answers
Answer:
the the 3rd one Is the one
Related Questions
Help please:))
2. When shipping ice cream, melting is understandably a big concern. You will notice that ice cream is not generally packaged in a cube-shaped container. A standard container of ice cream contains 1 L, or 1000 cm3 of ice cream,
a. What would be the optimal dimensions (radius and height) to minimize surface area?
b. What would the surface area be?
C. Suggest at least two reasons why this is different from the ice cream packaging that you see in the stores.
Answers
Answer:
a) Because this asks about the radius and height, I assume that we are talking about a cylinder shape.
Remember that for a cylinder of radius R and height H the volume is:
V = pi*R^2*H
And the surface will be:
S = 2*pi*R*H + pi*R^2
where pi = 3.14
Here we know that the volume is 1000cm^3, then:
1000cm^3 = pi*R^2*H
We can rewrite this as:
(1000cm^3)/pi = R^2*H
Now we can isolate H to get:
H = (1000cm^3)/(pi*R^2)
Replacing that in the surface equation, we get:
S = 2*pi*R*H + pi*R^2
S = 2*pi*R*(1000cm^3)/(pi*R^2) + pi*R^2
S = 2*(1000cm^3)/R + pi*R^2
So we want to minimize this.
Then we need to find the zeros of S'
S' = dS/dR = -(2000cm^3)/R^2 + 2*pi*R = 0
So we want to find R such that:
2*pi*R = (2000cm^3)/R^2
2*pi*R^3 = 2000cm^3
R^3 = (2000cm^3/2*3.14)
R = ∛(2000cm^3/2*3.14) = 6.83 cm
The radius that minimizes the surface is R = 6.83 cm
With the equation:
H = (1000cm^3)/(pi*R^2)
We can find the height:
H = (1000cm^3)/(3.14*(6.83 cm)^2) = 6.83 cm
(so the height is equal to the radius)
b) The surface equation is:
S = 2*pi*R*H + pi*R^2
replacing the values of H and R we get:
S = 2*3.14*(6.83 cm)*(6.83 cm) + 3.14*(6.83 cm)^2 = 439.43 cm^2
c) Because if we pack cylinders, there is a lot of space between the cylinders, so when you store it, there will be a lot of space that is not used and that can't be used for other things.
Similarly for transport problems, for that dead space, you would need more trucks to transport your ice cream packages.
wrote the terms below.
–8, –4, 0, 4, 8, 12
What do these terms represent?
an arithmetic series
an arithmetic sequence
a geometric series
a geometric sequence
Answers
Answer:
an arithmetic sequence
Step-by-step explanation:
an arithmetic series is wrong also heres an example i found of an arithmetic sequence
The terms in the given sequence represents an arithmetic sequence.
What is Arithmetic Sequence?Arithmetic sequence is a sequence of numbers where the numbers are arranged ion a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference which is commonly denoted by the letter 'd'.
Given sequence of numbers is,
-8, -4, 0, 4, 8, 12, ......
We have to find which sequence does it represent.
This is not a series since they are not represented as the sum.
If the sequence is a geometric sequence, then the ratio of consecutive numbers will be same.
If it is arithmetic sequence, then the difference of consecutive numbers will be same.
Here, ratio is not same.
Difference are same.
-4 - -8 = 4, 0 - -4 = 4, 4 - 0 = 4, 8 - 4 = 4, ........
Common difference is 4.
Hence it is an arithmetic sequence.
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Can someone please help me?
Answers
you have to read the bottom link for the answer key
A random sample of n1 = 296 voters registered in the state of California showed that 146 voted in the last general election. A random sample of n2 = 215 registered voters in the state of Colorado showed that 127 voted in the most recent general election. Do these data indicate that the population proportion of voter turnout in Colorado is higher than that in California? Use a 5% level of significance.
Answers
Answer:
The p-value of the test is 0.0139 < 0.05, which means that these data indicates that the population proportion of voter turnout in Colorado is higher than that in California.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes 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]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
California:
Sample of 296 voters, 146 voted. This means that:
[tex]p_{Ca} = \frac{146}{296} = 0.4932[/tex]
[tex]s_{Ca} = \sqrt{\frac{0.4932*0.5068}{296}} = 0.0291[/tex]
Colorado:
Sample of 215 voters, 127 voted. This means that:
[tex]p_{Co} = \frac{127}{215} = 0.5907[/tex]
[tex]s_{Co} = \sqrt{\frac{0.5907*0.4093}{215}} = 0.0335[/tex]
Test if the population proportion of voter turnout in Colorado is higher than that in California:
At the null hypothesis, we test if it is not higher, that is, the subtraction of the proportions is at most 0. So
[tex]H_0: p_{Co} - p_{Ca} \leq 0[/tex]
At the alternative hypothesis, we test if it is higher, that is, the subtraction of the proportions is greater than 0. So
[tex]H_1: p_{Co} - p_{Ca} > 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the two samples:
[tex]X = p_{Co} - p_{Ca} = 0.5907 - 0.4932 = 0.0975[/tex]
[tex]s = \sqrt{s_{Co}^2+s_{Ca}^2} = \sqrt{0.0291^2+0.0335^2} = 0.0444[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{0.0975 - 0}{0.0444}[/tex]
[tex]z = 2.2[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a difference above 0.0975, which is 1 subtracted by the p-value of z = 2.2.
Looking at the z-table, z = 2.2 has a p-value of 0.9861.
1 - 0.9861 = 0.0139.
The p-value of the test is 0.0139 < 0.05, which means that these data indicates that the population proportion of voter turnout in Colorado is higher than that in California.
An industrial psychologist consulting with a chain of music stores knows that the average number of complaints management receives each month throughout the industry is 4, but the variance is unknown. Nine of the chain's stores were randomly selected to record complaints for one month; they received 2, 4, 3, 5, 0, 2, 5, 1, and 5 complaints. Using the .05 significance level, is the number of complaints received by the chain different from the number of complaints received by music stores in general?
1. Use the five steps of hypothesis testing.
2. Sketch the distributions involved
3. Explain the logic of what you did to a person who is familiar with hypothesis testing, but knows nothing about t tests of any kind. Be sure to explain how this problem differs from a problem with a known population variance and a single sample.
Answers
Answer: See explanation
Step-by-step explanation:
1. Use the five steps of hypothesis testing.
Step 1: The aim of the research is to conduct the five steps of hypothesis testing.
Step 2:
Null hypothesis: H0 u= 4
Population mean: H1 u = 4
Alternate hypothesis: u ≠ 4
Population mean: u ≠ 4
Step 3 and step 4 are attached.
Step 5: Based on the calculation, the calculated value of t is less than the t critical value, therefore, the null hypothesis will be failed to be rejected.
2. Sketch the distributions involved
This has been attached.
3. Explain the logic of what you did to a person who is familiar with hypothesis testing, but knows nothing about t tests of any kind.
The distribution is "t".
The means is tested by using T-test.
Chi-square is used to test the single variance.
79
Work out the circumference of this circle.
Take a to be 3.142 and write down all the digits given by your calculator.
14 cm
Answers
Answer: 43.988
Step-by-step explanation: The formula for the circumference of a circle is the diameter multiplied by pi. Since the diameter is 14 and it is telling us to use 3.142 as pi, we can multiply the two and get the answer.
Which of the following tables represent valid functions?
Answers
Answer:
Step-by-step explanation:
A relation may or may not represent a function.
Table (a), (c) and (d) represent a function
The tables represent a relation
For a relation to be a function, then:
The y values must have unique (or distinct) x-values.
From the list of tables, we have the following observations
All y values in table (a), have different corresponding x valuesy values 3 and 6 in table (b), point to the same x value (2)All y values in table (c), have different corresponding x valuesAll y values in table (d), have different corresponding x valuesHence, all the tables represent a valid function, except table (b)
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if the average of b and c is 8, and d=3b-4, what is the average of c and d in terms of b?
Answers
[tex] \underline{ \huge \mathcal{ Ànswér} } \huge: - [/tex]
Average of b and c is 8, that is
[tex]➢ \: \: \dfrac{b + c}{2} = 8[/tex]
[tex]➢ \: \: b + c = 16[/tex]
[tex]➢ \: \: c = 16 - b[/tex]
now let's solve for average of c and d :
[tex]➢ \: \: \dfrac{c + d}{2} [/tex]
[tex]➢ \: \: \dfrac{16 - b + 3b - 4}{2} [/tex]
[tex]➢ \: \: \dfrac{12 + 2b}{2} [/tex]
[tex]➢ \: \: \dfrac{2(6 + b)}{2} [/tex]
[tex]➢ \: \: b + 6[/tex]
Therefore, the average of c and d, in terms of b is : -
[tex] \large \boxed{ \boxed{b + 6}}[/tex]
[tex]\mathrm{✌TeeNForeveR✌}[/tex]
Answer:
b+6
Problem:
If the average of b and c is 8, and d=3b-4, what is the average of c and d in terms of b?
Step-by-step explanation:
We are given (b+c)/2=8 and d=3b-4.
We are asked to find (c+d)/2 in terms of variable, b.
We need to first solve (b+c)/2=8 for c.
Multiply both sides by 2: b+c=16.
Subtract b on both sides: c=16-b
Now let's plug in c=16-b and d=3b-4 into (c+d)/2:
([16-b]+[3b-4])/2
Combine like terms:
(12+2b)/2
Divide top and bottom by 2:
(6+1b)/1
Multiplicative identity property applied:
(6+b)/1
Anything divided by 1 is that anything:
(6+b)
6+b
b+6
A game consists of tossing three coins. If all three coins land on heads, then the player wins $75. If all three coins land on tails, then the player wins $45. Otherwise, the player wins nothing. On average, how much should a player expect to win each game
Answers
Answer:
On average, a player should expect to win $15.
Step-by-step explanation:
The expected value in an event with outcomes:
x₁, x₂, ..., xₙ
Each with probability:
p₁, ..., pₙ
is given by:
Ev = x₁*p₁ + ... +xₙ*pₙ
In this case we have 3 outcomes:
player wins $75 = x₁
player wins $45 = x₂
player does not win = x₃
Let's find the probabilities of these events.
player wins $75)
Here we must have the 3 coins landing on heads, so there is only one possible outcome to win $75
While the total number of outcomes for tossing 3 coins, is the product between the number of outcomes for each individual event (where the individual events are tossing each individual coin, each one with 2 outcomes)
Then the number total of outcomes is:
C = 2*2*2 = 8
Then the probability of winning $75 is the quotient between the number of outcomes to win (only one) and the total number of outcomes (8)
p₁ = 1/8
Win $45:
This happens if the 3 coins land on tails, so is exactly equal to the case above, and the probability is the same:
p₂ = 1/8
Not wining:
Remember that:
p₁ + p₂ + ... + pₙ = 1
Then for this case, we must have:
p₁ + p₂ + p₃ = 1
1/8 + 1/8 + p₃ = 1
p₃ = 1 - 1/8 - 1/8
p₃ = 6/8
Then the expected value will be:
Ev = $75*1/8 + $45*1/8 + $0*6/8 = $15
On average, a player should expect to win $15.
What is the value of y?
Answers
9514 1404 393
Answer:
(d) 2
Step-by-step explanation:
The parallel lines divide the transversals proportionally, so we have ...
3y/3 = 2y/y
y = 2 . . . . . . . . . simplify (assuming y ≠ 0)
Suppose 50.7 liters of water came out of a faucet today. If 2.6 liters of water come out each minute, for how many minutes was the faucet on?
Answers
al calls every 3 days, lee every 4 days, and pat every 6 day. Once every ? days, all three will call on the same day
Answers
Answer:
12
Step-by-step explanation:
Find the LCM (Least Common Multiple) of the three numbers.
We could multiply 3 x 4 x 6 to get 72, but there is a smaller multiple, 12.
6 x 2 = 12
4 x 3 = 12
3 x 4 = 12
Hope this helps!
i’ll make brainliest
look at the photo and check my work?
also tell me the answer to the ones i didn’t do
thanks :)
Answers
2. =, this is because in decimals 100% and 1 are the same.
3. Measure of center is the mean, median, and mode, as they are all ways to interpret the center of the data.
5. The lines do not appear to be congruent as they are of different lengths.
Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.
Select the correct statement about what data scientists do during the Data Preparation stage.
a. During the Data Preparation stage, data scientists define the variables to be used in the model.
b. During the Data Preparation stage, data scientists determine the timing of events.
c. During the Data Preparation stage, data scientists aggregate the data and merge them from different sources.
d. During the Data Preparation stage, data scientists identify missing data.
e. All of the above statements are correct.
Answers
Answer:
e. All of the above statements are correct.
Option e is correct. All of the above statements are correct.
What is Data science?Data science is an interdisciplinary academic field that uses statistics, scientific computing, scientific methods, processes, algorithms and systems to extract or extrapolate knowledge and insights from noisy, structured and unstructured data
Data Scientist makes value out of data, he is expert in various tools and technologies like machine learning, deep learning, artificial intelligence and he solve business problems by presenting a model to predict business future.
During data preparation, data scientists and DBAs aggregate the data and merge them from different sources. During data preparation, data scientists and DBAs define the variables to be used in the model.
Hence, All of the above statements are correct, Option e is correct.
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WILL MAKE BRAINLIEST
Answers
Answer:
x=3
Step-by-step explanation:
The ratios need to be the same
AB CB
---------- = ----------
AD ED
3 x
----- = ---------
3+9 12
3 x
----- = ---------
12 12
X must equal 3
a study of patients who were overweight found that 53% also had elevated blood pressure. If 3 overweight patients are selected find the probability that all three have elevated blood pressure
Answers
Answer:
14.8%
Step-by-step explanation:
53/100*53/100*53/100
Rubin grew 9 tomatoes with 6 seed packs. How many seed packs does Rubin need to have a total of 21 tomatoes in his garden?
Answers
Answer: 14 seed packs
Step-by-step explanation:
You'd divide the 9 tomatoes by the 6 seed packs that were necessary to grow them, resulting in 1.5 tomatoes per seed pack. Divide 21 by this 1.5 to find the number of seed packs needed to grow 21 tomatoes, which would be 14.
Draw clearly the graph of the linear equation. y=1/2x, where x= (-4 -2, 0, 2, 4)
Answers
Answer:
(in attachment)
Step-by-step explanation:
you can find the points by inputting the x-values into the equation to solve for the y-values, then connecting the plotted points to create the line.
When x=-4
y=1/2(-4)
y=-2
(-4,-2)
Repeat for all values.
A solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x + 2) cm.
A solid oblique pyramid has a square base with edges measuring x centimeters. The height is (x + 2) centimeters.
Which expression represents the volume of the pyramid?
StartFraction x cubed + 2 x squared Over 3 EndFraction cm3
StartFraction x squared + 2 x squared Over 2 EndFraction cm3
StartFraction x cubed Over 3 EndFraction cm3
StartFraction x cubed + 2 x squared Over 2 EndFraction cm3
Answers
Answer:
Hello,
Answer A StartFraction x cubed + 2 x squared Over 3 EndFraction cm3
Step-by-step explanation:
[tex]V=x^2*\dfrac{x+2}{3} \\\\\boxed{V=\dfrac{x^3+2x^2}{3} }\\[/tex]
the third of the sum of the cube of x and double of the square of x ( cm³)
The Volume of pyramid with a square base of side x cm and height of (x + 2) cm is (x³ + 2x²) / 3
What is volume?
Volume is the amount of space occupied by a three dimensional shape or object.
Area of the square base = x * x = x² cm²
Volume of pyramid = (1/3) * area of base * height = (1/3) * x² * (x + 2)
Volume of pyramid = (x³ + 2x²) / 3
The Volume of pyramid with a square base of side x cm and height of (x + 2) cm is (x³ + 2x²) / 3
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HELPPPP
what is this
Answers
Answer:
Pls be specific with your question
HELPPP PLEASE ASAP!!! I don’t know how to solve this problem nor where to start? Can some please help me out and explain how you got the answer please. Thank you for your time.
Answers
Step-by-step explanation:
Count the number of times you have to move the decimal point to the right until it is to the right of the 1st nonzero number.
a) You have to move the decimal point 11 times until it gets to the right of the 1st nonzero number, which is 7. You then rewrite this number as
[tex]7.2×10^{-11}[/tex]
The exponent of 10 is a negative number because you moved the decimal point to the right.
b) Similarly, you have to move the point 9 times to the right so the answer is
[tex]9.5×10^{-9}[/tex]
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 444 gram setting. It is believed that the machine is underfilling the bags. A 41 bag sample had a mean of 440 grams with a variance of 441. Assume the population is normally distributed. A level of significance of 0.05 will be used. Specify the type of hypothesis test.
Answers
Answer:
The null hypothesis is [tex]H_0: \mu = 444[/tex]
The alternative hypothesis is [tex]H_1: \mu < 444[/tex]
The p-value of the test is 0.1148 > 0.05, which means that the sample does not give enough evidence to conclude that the machine is underfilling the bags.
Step-by-step explanation:
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 444 gram setting.
At the null hypothesis, we test if the machine works correctly, that is, the mean is of 444. So
[tex]H_0: \mu = 444[/tex]
At the alternative hypothesis, we test if they are underfilling, that is, if the mean is of less than 444. So
[tex]H_1: \mu < 444[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
444 is tested at the null hypothesis:
This means that [tex]\mu = 444[/tex]
A 41 bag sample had a mean of 440 grams with a variance of 441.
This means that [tex]n = 41, X = 440, s = \sqrt{441} = 21[/tex]
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{440 - 444}{\frac{21}{\sqrt{41}}}[/tex]
[tex]t = -1.22[/tex]
P-value of the test:
Right-tailed test(test if the mean is less than a value), with 41 - 1 = 40 df and t = -1.22.
Using a t-distribution calculator, this p-value is of 0.1148
The p-value of the test is 0.1148 > 0.05, which means that the sample does not give enough evidence to conclude that the machine is underfilling the bags.
A group of 120 students were surveyed about their interest in a new International Studies program. Interest was measured in terms of high, medium, or low. 30 students responded high interest; 50 students responded medium interest; 40 students responded low interest. What is the relative frequency of students with high interest? A. 30% B. 36.4% C. 25% D. Cannot be determined. Group of answer choices
Answers
Answer:
Option C (25%) is the correct answer.
Step-by-step explanation:
Given:
Number of students,
= 120
Students responded high interest,
= 30
Students responded medium interest,
= 50
Students responded low interest,
= 40
Now,
The relative frequency will be:
= [tex]\frac{30}{120}[/tex]
= [tex]0.25[/tex]
or,
= [tex]25[/tex]%
Answer this please~!!!!
Answers
Answer:
12
Step-by-step explanation:
113.04=3.14 x 3^2 x h/3
Given a set of data that is skewed-left, there is at least _____ % of the data within 2 standard deviations.
Answers
Answer:
75
Step-by-step explanation:
For non-normal distributions, we use Chebyshev's Theorem.
Chebyshev Theorem
The Chebyshev Theorem states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
In this question:
Within 2 standard deviations of the mean, so 75%.
Rudy Banks has won $5000 to attend university. If he invests the money in an
account at 12% per annum, compounded monthly, how much can he draw monthly
for the next 3 years?
Answers
Answer:
$7153.84
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Compounded Interest Rate Formula: [tex]\displaystyle A = P(1 + \frac{r}{n})^{nt}[/tex]
P is principle amountr is raten is compound ratet is timeStep-by-step explanation:
Step 1: Define
Identify variables
P = 5000
r = 12% = 0.12
n = 12
t = 3
Step 2: Find Interest
Substitute in variables [Compounded Interest Rate Formula]: [tex]\displaystyle A = 5000(1 + \frac{0.12}{12})^{12(3)}[/tex][Exponents] Multiply: [tex]\displaystyle A = 5000(1 + \frac{0.12}{12})^{36}[/tex](Parenthesis) Add: [tex]\displaystyle A = 5000(1.01)^{36}[/tex]Evaluate exponents: [tex]\displaystyle A = 5000(1.43077)[/tex]Multiply: [tex]\displaystyle A = 7153.84[/tex]A teacher calculates for the test grades in
Class A, mean = 32 and sd = 4
Class B, mean = 32 and sd = 8
a. If the teacher was going to guess what any student in his/her class would earn, what is the best score
to guess?
b. Which of the classes has more consistency in their scores? Why?
Answers
Answer:
a. best score to guess would be 33
b. Standard deviation simplifies the square root of the mean so makes it closer to 1 has more consistency as the mean of 32 when squared is sqrt 32 is Class A as class a = 4 and is closer to 5.65685425
as 5.65685425^2 = 32
Step-by-step explanation:
If you are comparing two normally-distributed variables on the same measurement scale then yes, you can regard the standard deviation as an indicator of how reliable the mean is--the smaller the standard deviation, the better able you are to "zero in" on the actual population mean.
a. proofs;
We find 32/6 = 5.333 and 32/5 = 6.4 and 6.4 is closer to both sd 4 and 8 than 5.33 is. As 6.4 it is closer to 6
But when we use 33/6 = 5.5 and therefore shows close range 6
therefore the two sd proves it is slightly high 32 score average for both classes A + B when joined and high 32 = 33 mean when classes A+B are joined or you could say 32/8 = 4 is class B becomes lower tests scores as 32/4 = 8 of class A that has higher test scores.
In this exercise we have to use probability and statistics to organize the students' grades, so we have:
A) best score is 33
B) Class A
In the first part of the exercise we have to analyze the grades of each class, like this:
A)Class A: 32/4
Class B: 32/8
Dividing each of them we have:
[tex]32/4=8 \\32/8=4[/tex]
B) With the information given above, we can say that the best class is A.
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An isosceles right triangle has a hypotenuse that measures 4√2 cm. What is the area of the triangle?
Answers
Answer:
It would be B. 16 centimeters^2
Step-by-step explanation:
What is the solution to the inequality -6+|2p+3| > 7
Answers
Step-by-step explanation:
you're going to have to set up two expressions since it's an absolute value problem
The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.02 level that the medicine relieves pain in more than 384 seconds. For a sample of 41 patients, the mean time in which the medicine relieved pain was 387 seconds. Assume the population standard deviation is 23. Find the P-value of the test statistic.
Answers
Answer:
The p-value of the test statistic is 0.2019.
Step-by-step explanation:
Test if there is evidence at the 0.02 level that the medicine relieves pain in more than 384 seconds.
At the null hypothesis, we test if it relieves pain in at most 384 seconds, that is:
[tex]H_0: \mu \leq 384[/tex]
At the alternative hypothesis, we test if it relieves pain in more than 384 seconds, that is:
[tex]H_1: \mu > 384[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
384 is tested at the null hypothesis:
This means that [tex]\mu = 384[/tex]
For a sample of 41 patients, the mean time in which the medicine relieved pain was 387 seconds. Assume the population standard deviation is 23.
This means that [tex]n = 41, X = 387, \sigma = 23[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{387 - 384}{\frac{23}{\sqrt{41}}}[/tex]
[tex]z = 0.835[/tex]
P-value of the test:
The p-value of the test is the probability of finding a sample mean above 387, which is 1 subtracted by the p-value of z = 0.835.
Looking at the z-table, z = 0.835 has a p-value of 0.7981.
1 - 0.7981 = 0.2019
The p-value of the test statistic is 0.2019.
