Answer:
There is not enough evidence to support the claim that your team scored an average significantly less than 110 points.
Step-by-step explanation:
The question is incomplete:
There is no data from the sample.
We will use the sample [105 107 117 106 110 ] as an example to solve the question.
The mean of the sample is:
[tex]M=\dfrac{1}{5}\sum_{i=1}^{5}(105+107+117+106+110)\\\\\\ M=\dfrac{545}{5}=109[/tex]
The standard deviation of the sample is:
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{5}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}\cdot [(105-(109))^2+(107-(109))^2+(117-(109))^2+(106-(109))^2+(110-(109))^2]}\\\\\\ s=\sqrt{\dfrac{1}{4}\cdot [(16)+(4)+(64)+(9)+(1)]}\\\\\\ s=\sqrt{\dfrac{94}{4}}=\sqrt{23.5}\\\\\\s=4.848[/tex]
This is a hypothesis test for the population mean.
The claim is that your team scored an average significantly less than 110 points.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=110\\\\H_a:\mu< 110[/tex]
The significance level is 0.01.
The sample has a size n=5.
The sample mean is M=109.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=4.848.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{4.848}{\sqrt{5}}=2.17[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{109-110}{2.17}=\dfrac{-1}{2.17}=-0.46[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=5-1=4[/tex]
This test is a left-tailed test, with 4 degrees of freedom and t=-0.46, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-0.46)=0.334[/tex]
As the P-value (0.334) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that your team scored an average significantly less than 110 points.
h(1)=0. h(n)=h(n-1)-9 explicit formula for h(n)=
Answer:
0-9(n-1)
Step-by-step explanation:
We can tell the first term of the sequence is 0 and the common difference is -9. So the explicit formula would be h(n)=0-9(n-1)
The explicit formula for h(n) comes to be h(n)=9-9n.
What is an arithmetic progression?An arithmetic progression is a list of numbers where the difference between consecutive terms is always constant.
[tex]h(n)=h(n-1)-9[/tex]
[tex]h(n)-h(n-1)=-9[/tex]
So the common difference of the arithmetic progression will be -9.
[tex]h(1)=0[/tex] means the first term of the AP is 0.
We know that [tex]n^{th}[/tex] term of an AP is given by:
[tex]h(n)=a+(n-1)d[/tex]
Where a is the first term and d is a common difference.
Fo the given series [tex]a=0[/tex] and [tex]d=-9[/tex]
So, [tex]h(n)=0+(n-1)(-9)[/tex]
[tex]h(n)=9-9n[/tex]
So, the explicit formula for h(n) is [tex]h(n)=9-9n[/tex]
Hence, the explicit formula for h(n) comes to be [tex]h(n)=9-9n[/tex].
To get more about arithmetic progressions visit:
https://brainly.com/question/6561461
Classify the following triangle. Check ALL that apply.
Twenty percent of adults in a particular community have at least a​ bachelor's degree. Suppose x is a binomial random variable that counts the number of adults with at least a​ bachelor's degree in a random sample of 100 adults from the community. If you are using a calculator with the binompdf and binomcdf​ commands, which of the following is the most efficient way to calculate the probability that more than 60 adults have a​ bachelor's degree, ​P(x?>60)?
a. P(x < 60)=binompdf(100,0 20,59)
b. P(x<60)=binompdf(100.0.20.60)
c. P(x<60)= binomcdf(100,0,20,59)
d. P(x<60)=binomcdf (100.0.20.60)
Answer:
Step-by-step explanation:
Since we are dealing with binomial probability in this scenario, then the outcome is either a success or a failure. A success in this case means that a chosen adult has a bachelor's degree. The probability of success, p would be 20/100 = 0.2
The number of adults sampled, n is 100
The number of success, x is 60
The probability that more than 60 adults have a bachelor's degree P(x >60) would be represented as
d. P(x<60)=binomcdf (100.0.20.60)
binompdf is used when we want to determine P(x = 60)
Cory is picking out some movies to rent, and he is primarily interested in comedies and horror films. He has narrowed down his selections to 14 comedies and 19 horror films. How many different combinations of 4 movies can he rent if he wants at least one comedy
Answer:
37044 different combinations of 4 movies can he rent if he wants at least one comedy
Step-by-step explanation:
The order in which the movies are selected is not important, so we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
How many different combinations of 4 movies can he rent if he wants at least one comedy
The easier way to solve this is subtract the total from the number of combinations with no comedies.
Total:
4 movies from a set of 14 + 19 = 33. So
[tex]C_{33,4} = \frac{33!}{4!(33-4)!} = 40920[/tex]
No comedies:
4 movies from a set of 19.
[tex]C_{19,4} = \frac{19!}{4!(19-4)!} = 3876[/tex]
At least one comedy:
40920 - 3876 = 37044
37044 different combinations of 4 movies can he rent if he wants at least one comedy
Write out the sample space for the given experiment. Use the following letters to indicate each choice: Y for yellow, B for blue, W for white, G for gray, T for teak, and U for unfinished. While renovating your house, you have a choice of paint colors for your game room: yellow, blue, or white. You also have the following options for the finish on your entertainment center: gray, teak, or unfinished.
Answer:
YG, YT, YU, BG, BT, BU, WG, WT and WU
Step-by-step explanation:
The sample space are all the posibles options that you can take, so the sample space in these case is:
YG, YT, YU, BG, BT, BU, WG, WT and WU
Where, for example, YG means that you choose Yellow for your game room and Green for your entertainment center and BU means that you chosse Yellow for your game room and Unfinished for your entertainment center.
Suppose a jar contains 10 red marbles and 34 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
Answer:
The probability that both are red is [tex]P(red\:and \:red)=\frac{45}{946}\approx0.04756\approx4.756\%[/tex].
Step-by-step explanation:
Probability is simply how likely something is to happen and its given by
Probability of an event = (# of ways it can happen) / (total number of outcomes)
Two events are dependent when the outcome of the first event influences the outcome of the second event. The probability of two dependent events is the product of the probability of X and the probability of Y AFTER X occurs.
[tex]P(A\:and\: B)=P(A)\cdot P(A|B)[/tex]
At our first pull, there is an [tex]P(red)=\frac{10}{10+34}[/tex] chance that a red will be pulled.
At the second pull there is a [tex]P(red)=\frac{9}{9+34}[/tex] chance that the second marble will be red.
Therefore, the probability that both are red is
[tex]P(red\:and \:red)=\frac{10}{10+34}\cdot \frac{9}{9+34}=\frac{45}{946}\approx0.04756\approx4.756\%[/tex]
A recent study reported that 22% of adults in France admitted to texting or e-mailing while driving. A random sample of 110 French adults was randomly selected. What is the probability that 26 or more of these adults admitted to admitted to texting or e-mailing while driving?
Answer:
Step-by-step explanation:
ported that 22% of adults in France admitted to texting or e-mailing while driving. A random sample of 110 French adults was randomly selected. What is the probability that 26
Using a binomial distribution with mean = n*p = 110*0.22 = 24.2 and variance = n*p*(1-p) = 24.2*(1-0.22) = 18.876
Approximating it to a normal distribution,
[tex]P(x\geq 26)\\\\=P(Z\geq \frac{26-24.2}{\sqrt{18.876} } )\\\\=P(Z\geq 0.41)\\\\=0.3481[/tex]
QUESTION OF
Factor y2 - 12y + 36
А
(y + 6)(y-6)
(y + 6)(y + 6)
(y-6)(y + 6)
(y-6)(y-6)
Answer:
(y-6)(y-6)
Step-by-step explanation:
y^2 - 12y + 36= y^2-2*6y+6^2= (y-6)^2= (y-6)(y-6)
Answer:
[tex](y-6)(y-6)[/tex]
Step-by-step explanation:
[tex]y^2 - 12y + 36[/tex]
[tex]y^2-6y-6y+36[/tex]
[tex]y(y-6)-6(y-6)[/tex]
[tex](y-6)(y-6)[/tex]
permutations and combination question ^^
Answer: choice B
Step-by-step explanation:
50C40
=50C10
=50!/40!*10!
According to a survey conducted by the Associated Press (AP) and petside in 2009, 63% of dog owners and 53% of cat owners would be at least somewhat likely to give CPR to their pet in the event of a medical emergency. The survey involved a nationwide sample of 1,166 pet owners. Use this information to answer the following questions.
Requried:
a. Produce a well-labeled segmented bar graph to display these percentages.
b. Identify the two categorical variables displayed in the graph.
c. What additional information would you need in orde to construct a 2 x 2 table?
Answer:
a) Check the bar graph in the picture attached
b) The two categorical variables are:
1) Type of owners
2) Likelihood to give CPR
c) Information on the population( in number or percentage) of the dog/cat owners.
Step-by-step explanation:
a) the bar chart is drawn with % of owners likely to give CPR to their pets on the y-axis and the owner types on the x - axis.
b) The two categorical variables are:
1) Type of owners
2) Likelihood to give CPR
c) To construct a 2 x 2 table, the percentage (or number) of either dog owners or cat owners.
Since we know that the total number of pet owners that were sampled = 1166.
If the number of dog owners is known, it can be subtracted from the total number of pet owners to know the number of cat owners and vice versa. If this information is gotten, then the 2 x 2 table can be constructed.
.If 3x+ 6 = 5x -10,then the value of x is
Answer:
X=8
Step-by-step explanation:
3x+ 6 = 5x -10
6+10=5X-3X
16=2X
X=8
Suppose a batch of metal shafts produced in a manufacturing company have a variance of 2.89 and a mean diameter of 211 inches. If 86 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches
Answer:
27.58% probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [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.
In this question, we have that:
[tex]\mu = 211, \sigma = \sqrt{2.89} = 1.7, n = 86, s = \frac{1.7}{\sqrt{86}} = 0.1833[/tex]
What is the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches.
Either greater than 211 + 0.2 = 211.2 or smaller than 211 - 0.2 = 210.8. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.
Probability of being less than 210.8:
This is the pvalue of Z when X = 210.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{210.8 - 211}{0.1833}[/tex]
[tex]Z = -1.09[/tex]
[tex]Z = -1.09[/tex] has a pvalue of 0.1379
Probability of differing from the population mean by greater than 0.2 inches :
2*0.1379 = 0.2758
27.58% probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches
Answer:
Probability is 86.24%
Step-by-step explanation:
We can solve this by using the Z-score formula.
Z = (X - μ)/σ
Where;
μ is mean = 211 inches
σ is standard deviation
Now, we are given variance as 2.89
Formula for standard deviation using variance is;
SD = √variance
SD = √2.89
SD = 1.7
To find the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches, we will find the p-value of z and subtract 1 from it.
Since we are told that the sample shafts would differ by 0.2 inches, thus;
X = 211 + 0.2 = 211.2
Since we are working with sample mean of 86, then we have;
Z = (X - μ)/s
s = σ/√86
s = 1.7/√86
s = 0.1833
So,
Z = (211.2 - 211)/0.1833
Z = 1.0911
From z-score calculator, the p-value is gotten to be 0.1376
Thus, probability that mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches is;
Probability = 1 - 0.1376 = 0.8624 = 86.24%
Find the product in simplest form. (3√2) ( √10) 3 √10 3 √20 6 √5 6 √10
Answer:
6 sqrt(5)
Step-by-step explanation:
(3√2) ( √10)
We know that sqrt(a) * sqrt(b) = sqrt(ab)
3 sqrt(2*10)
3 sqrt(20)
3 sqrt(4*5)
We know that sqrt(a) * sqrt(b) = sqrt(ab)
3 sqrt(4) sqrt(5)
3 * 2 * sqrt(5)
6 sqrt(5)
What is (x+2)(x+5) in polynomial standard form
Answer:
=x^2+7x+10
Step-by-step explanation:
Simplify: xx+5x+2x+2.5: x+7x+10
Add similar elements: 5x+2x= 7x
=xx+7x+2.5
xx=x2
2.5=10
=x+7x+10
Answer: =x^2+7x+10
Hope this helps.
3. Show why, for linear functions, a vertical translation is equivalent to a horizontal
translation. For a linear function, what horizontal translation is equivalent to a vertical
translation of 3 units up?
4. Alex says that the function f(x) = (3x)represents a vertical stretch of the quadratic
parent function by a factor of 3. Marta says that it represents a horizontal compression
1
by a factor of 3. Decide whether one student is correct, both are correct, or neither is
correct.
5. For an unknown parent function f(x), write a function g(x) that is:
O
o vertically stretched by a factor of 2,
shifted up 5 units, and
o shifted right 4 units.
6. Explain how your function accomplishes these transformations.
Answer:
3. Vertical is the same as horizontal for linear equations because when moving the function up, it moves the whole line left along the x-axis too. When moving it down, it moves the equation right on the x-axis.
4. Alex is correct
5. g(x)=(2x-8)^2+5
6. This accomplishes these transformations because I made a graph about it
Step-by-step explanation:
The average weight of the entire batch of the boxes of cereal filled today was 20.5 ounces. A random sample of four boxes was selected with the following weights: 20.05, 20.56, 20.72, and 20.43. The sampling error for this sample is ________.
Answer:
[tex] s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
And replacing we got:
[tex] s= 0.286[/tex]
And then the estimator for the standard error is given by:
[tex] SE= \frac{0.286}{\sqrt{4}}= 0.143[/tex]
Step-by-step explanation:
For this case we have the following dataset given:
20.05, 20.56, 20.72, and 20.43
We can assume that the distribution for the sample mean is given by:
[tex] \bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
And the standard error for this case would be:
[tex] SE= \frac{\sigma}{\sqrt{n}}[/tex]
And we can estimate the deviation with the sample deviation:
[tex] s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
And replacing we got:
[tex] s= 0.286[/tex]
And then the estimator for the standard error is given by:
[tex] SE= \frac{0.286}{\sqrt{4}}= 0.143[/tex]
A county commissioner must vote on a resolution that would commit substantial resources to the construction of a sewer in an outlying residential area. Her fiscal decisions have been criticized in the past, so she decides to take a survey of residents in her district to find out whether they favor spending money for a sewer system. She will vote to appropriate funds only if she can be reasonably sure that a majority of the people in her district favor the measure. What hypotheses should she test?
Answer:
Step-by-step explanation:
This is a hypothesis testing involving population proportion. The null hypothesis would be that fewer than or 50% of the people would favor spending money for a sewer system. Since she will vote to appropriate funds only if she can be reasonably sure that a majority of the people in her district favor the measure, then the alternative hypothesis which she should test is that more than 50% of the people would favor spending money for a sewer system.
I need help one question 10 A to E
Answer:
Answers are below
Step-by-step explanation:
10a) Find how many multiples of 3 there are 4/12 = 1/3
10b) Find how many factors of 12 there are 6/12 = 1/2
10c) Find how many prime numbers there are 5/12
10d) 3/12 = 1/4
10e) Find how many numbers are less than 12 11/12
The equation of a circle is given below.
(x+12)^{2}+(y-9)^{2} = 35(x+12)
2
+(y−9)
2
=35left parenthesis, x, plus, 12, right parenthesis, squared, plus, left parenthesis, y, minus, 9, right parenthesis, squared, equals, 35
What is its center
Answer:
Center is [tex](-12,9)[/tex]
Step-by-step explanation:
Given: Equation of a circle is [tex](x+12)^2+(y-9)^2=35[/tex]
To find: center of the circle
Solution:
A circle is a locus of all points which are at equidistant from the fixed point (center).
Equation of a circle is of form [tex](x-a)^2+(y-b)^2=r^2[/tex] where [tex](a,b)[/tex] represents center of the circle and r denotes radius of the circle.
Given equation is [tex](x+12)^2+(y-9)^2=35[/tex]
[tex]\left [ x-(-12) \right ]^2+(y-9)^2=35[/tex]
Compare this equation with [tex](x-a)^2+(y-b)^2=r^2[/tex]
Center is [tex](a,b)=(-12,9)[/tex]
Answer:
The raidus is 5.92
Step-by-step explanation:
A triangular prism has a triangular base with dimensions of 3" by 4" by 5"
and a volume of 210 in? What is the surface area of the triangular prism?
Answer:
432in²Step-by-step explanation:
Volume of a triangular based prism = [tex]Base\ area * height[/tex]
Base area = Area of the triangle = 1/2 * base of the triangle * height of the triangle
Since the triangular base has dimensions of 3" by 4" by 5", then it is a right angled triangle with base of 4in and height of 3in
Base Area = 1/2 * 3 * 4
Base Area = 6in²
Substituting the volume and the base area value in the formula to get the height of the prism we have;
210 = 6H
H = 210/6
H = 35in
Surface area of the triangular prism = bh + pH
b= base of the triangle = 4in
h- height of the triangle = 3in
p= perimeter of the triangle = 3+4+5 = 12in
H= height of the prism = 35in
Surface area of the triangular prism = 4(3)+12(35)
Surface area of the triangular prism = 12+420in
Surface area of the triangular prism = 432in²
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. Show your work OR give an explaination.
Answer:
A: f(x) = (3/4 x)^2 - 1
Step-by-step explanation:
As you can see in the first image i attached, option A is the function that matches the one in your image. the "- 1" in the function is the y-intercept, and the 3/4 is what stretches your parabola which made it larger. You could also use process of elimination to get rid of option B and D since the y-intercepts do not match. Then you are left with A and C. the 4 in "(4x)^2" would make the parabola shrink, as you can see in the second image.
In the USA today internet poll 73 percent of readers indicated that they were satisfied with their lives.
1. 73 percent of readers are satisfied with their lives.
A. The population B. The sample
C. a population statistic D. a sample statistic
Answer:
c) Population parameter or Population statistic
Step-by-step explanation:
Population:-
The totality of observation with which we are concerned , whether this number be finite or infinite is called population
Sample :
A sample is subset of a Population
Given data the USA today internet poll is called Population
Given data 73 percent of readers are satisfied with their lives.
This is called Population parameter.
Write the following sentence as an equation.
The quotient of 120 and twice 20 is equal to 3.
Answer:
Check the answer. 1. ... 5 times a number plus 8 is equal to 3 times the number minus 4. 7 times a ... Twice a number is equal to 5 times the sum of the number and 6. The product ... If the equation is an identity, write the answer as “All real numbers.
Step-by-step explanation:
[Pic] Name a face of the solid.
Answer:
Option C.
Step-by-step explanation:
Solid in the given picture is a rectangular prism and a rectangular prism has 6 faces. Each face is formed by joining 4 vertices of the prism.
All the faces joining four vertices are: AFGB, BGHC, ADEF, DCHE, FEHG, ADCB.
From the given options,
Option (C). ADEF will be one of the face of the solid.
(2/5 + 3/4) x [ 3 - (1/4 : 1/5)]
Answer & Step-by-step explanation:
(2/5 + 3/4) * [ 3 - (1/4 : 1/5)]
When you see this sign, : , it usually means to divide the numbers because they represent some form of a ratio. So, we will divide 1/4 by 1/5.
First, do all of the operations in the parentheses ().
(2/5 + 3/4)*[ 3 - (1/4 : 1/5)]
(23/20) * [ 3 - (5/4)]
(23/20) * (7/4)
Now, we multiply 23/20 by 7/4.
(23/20) * (7/4)
161/80
This number can not be simplified so we will keep it as it is.
So, the answer to this expression is 161/80
At a certain car dealership, the probability that a customer purchases an SUV is . Given that a customer purchases an SUV, the probability that it is black is . What is the probability that a customer purchases a black SUV? Round your answer to four decimal places, if necessary.
Answer:
The probability that a customer purchases a black SUV is 0.05.
Step-by-step explanation:
The question is incomplete:
At a certain car dealership, the probability that a customer purchases an SUV is 0.20. Given that a customer purchases an SUV, the probability that it is black is 0.25.
The probability that a customer purchases a black SUV can be calculated as the multiplication of this 2 factors:
The probability of a customer purchasing a SUV: P(SUV).The probability that it is black, given that he or she purchases a SUV (conditional probabilty): P(B|SUV)We know then:
[tex]P(SUV)=0.25\\\\P(B | SUV)=0.20[/tex]
We can now calculate the probability as:
[tex]P(B\,\&\,SUV)=P(B|SUV)\cdot P(SUV)=0.25\cdot0.20=0.05[/tex]
Question 7 of 10
2 Points
Which number produces a rational number when multiplied by 0.5%
A. V
C. -1.73205089
O D. 0.54732814
BUBMIT
please help me, i dont understand
Answer:
OK so we can see that when x increases y does too. The answer is C
You stand a known distance from the base of the tree, measure the angle of elevation the top of the tree to be 15◦ , and then compute the height of the tree above eye level. Use the appropriate linear approximation to estimate the maximum possible error in your measurement of the angle (measuered in degrees) to be sure that your computation of the height has a relative error of at most ±p%. Give an exact answer, simplified as much as possible. Do not use a calculator. Assume p ∼ 0.
Answer:
The maximum possible error of in measurement of the angle is [tex]d\theta_1 =(14.36p)^o[/tex]
Step-by-step explanation:
From the question we are told that
The angle of elevation is [tex]\theta_1 = 15 ^o = \frac{\pi}{12}[/tex]
The height of the tree is h
The distance from the base is D
h is mathematically represented as
[tex]h = D tan \theta[/tex] Note : this evaluated using SOHCAHTOA i,e
[tex]tan\theta = \frac{h}{D}[/tex]
Generally for small angles the series approximation of [tex]tan \theta \ is[/tex]
[tex]tan \theta = \theta + \frac{\theta ^3 }{3}[/tex]
So given that [tex]\theta = 15 \ which \ is \ small[/tex]
[tex]h = D (\theta + \frac{\theta^3}{3} )[/tex]
[tex]dh = D (1 + \theta^2) d\theta[/tex]
=> [tex]\frac{dh}{h} = \frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta[/tex]
Now from the question the relative error of height should be at most
[tex]\pm p[/tex]%
=> [tex]\frac{dh}{h} = \pm p[/tex]
=> [tex]\frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta = \pm p[/tex]
=> [tex]d\theta = \pm \frac{\theta + \frac{\theta^3}{3} }{1+ \theta ^2} * \ p[/tex]
So for [tex]\theta_1[/tex]
[tex]d\theta_1 = \pm \frac{\theta_1 + \frac{\theta^3_1 }{3} }{1+ \theta_1 ^2} * \ p[/tex]
substituting values
[tex]d [\frac{\pi}{12} ] = \pm \frac{[\frac{\pi}{12} ] + \frac{[\frac{\pi}{12} ]^3 }{3} }{1+ [\frac{\pi}{12} ] ^2} * \ p[/tex]
=> [tex]d\theta_1 = 0.25 p[/tex]
Converting to degree
[tex]d\theta_1 = (0.25* 57.29) p[/tex]
[tex]d\theta_1 =(14.36p)^o[/tex]
A random sample of 100 pumpkins is obtained and the mean circumference is found to be 40.5 cm. Assuming that the population standard deviation is known to be 1.6 cm, use a 0.05 significance level to test the claim that the mean circumference of all pumpkins is equal to 39.9 cm.Do the following:_________.a) Write the hypotheses H0 and H1b) Calculate the z-scorec) Find corresponding probability to z-scoree) Write the decision and conclusion of the test of hypothesis.
Answer:
it should be 40.5 i believe
Step-by-step explanation:
