Answer:
a. P-value = 0.039.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the population mean significantly differs from 100.
b. P-value = 0.013.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the population mean significantly differs from 100.
c. P-value = 0.130.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the population mean significantly differs from 100.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the population mean significantly differs from 100.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=100\\\\H_a:\mu\neq 100[/tex]
The significance level is 0.05.
The sample has a size n=65.
The degrees of freedom for this sample size are:
[tex]df=n-1=65-1=64[/tex]
a. The sample mean is M=103.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=11.5.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{11.5}{\sqrt{65}}=1.4264[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{103-100}{1.4264}=\dfrac{3}{1.4264}=2.103[/tex]
This test is a two-tailed test, with 64 degrees of freedom and t=2.103, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t>2.103)=0.039[/tex]
As the P-value (0.039) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the population mean significantly differs from 100.
b. The sample mean is M=96.5.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=11.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{11}{\sqrt{65}}=1.3644[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{96.5-100}{1.3644}=\dfrac{-3.5}{1.3644}=-2.565[/tex]
This test is a two-tailed test, with 64 degrees of freedom and t=-2.565, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t<-2.565)=0.013[/tex]
As the P-value (0.013) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the population mean significantly differs from 100.
c. The sample mean is M=102.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=10.5.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{10.5}{\sqrt{65}}=1.3024[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{102-100}{1.3024}=\dfrac{2}{1.3024}=1.536[/tex]
This test is a two-tailed test, with 64 degrees of freedom and t=1.536, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t>1.536)=0.130[/tex]
As the P-value (0.13) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the population mean significantly differs from 100.
Jason is collecting data on the number of books students read each year. What type of data is this?
a. Qualitative
b. Discrete quantitative
c. Continuous quantitative
d. None of the above
Answer:
b. Discrete quantitative
Step-by-step explanation:
Hope that helps
The type of data is Discrete data.
What is Discrete data?Discrete data is information that can only take certain values. These values don't have to be whole numbers (a child might have a shoe size of 3.5 or a company may make a profit of £3456.25 for example) but they are fixed values – a child cannot have a shoe size of 3.72!
When values in a data set are countable and can only take certain values, it is called discrete data.
For example, number of students in a class, number of players required in a team, Number of players participated in a race, etc
We can easily count the variables in a discrete data.
Hence, type of data is Discrete data.
Learn more about Discrete data here:
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In circle O, the length of radius OL is 6 cm and the length of arc LM is 6.3 cm. The measure of angle MON is 75°. Circle O is shown. Line segments L O , M O, and N O are radii. The length of L O is 6 centimeters. Angle M O N is 75 degrees. The measure of arc L M is 6.3 centimeters. Rounded to the nearest tenth of a centimeter, what is the length of arc LMN?
Answer:
The answer is "14.2 cm"
Step-by-step explanation:
In the given question an attachment file is missing, by searching the question we find the solution, and we calculates the given value it will give the length of LMN, that is "14.2".
That's why its final answer is "14.2 cm".
Answer:
he answer is "14.2 cm"
Step-by-step explanation:
got it right on edg
(a) Which unit fraction 1/n for n s 50 has the decimal expansion of longest period?
(b) Justify your reasoning
Answer:
0.02
Step-by-step explanation:
If n is 50, 1/n is equivalent to 1/50. 1/50 as a decimal is 0.02.
If m is 21 inches, j is 28 inches, and ∠K measures 90°, then find k using the Law of Cosines. Round your answer to the nearest tenth.
Answer:
35 inches
Step-by-step explanation:
The right angle and the given measures in the ratio 3:4 tell you this is a 3:4:5 right triangle. k = 7·5 = 35 inches.
__
Using the Law of Cosines, ...
k² = m² +j² -2mj·cos(K)
k² = 21² +28² -2·21·28·cos(90°) = 441 +784 -0 = 1225
k = √1225 = 35
The length of k is 35 inches.
Answer:
35 Inches
Step-by-step explanation:
Instead of using the Law of Cosines, you can use the Pythagorean Theorem; or A^2 + B^2 = C^2 because angle K is 90 degrees. The equation would look like:
21^2 + 28^2 = C^2
441 + 784 = C^2 Square Each Term
1,225 = C^2 Simplify
35 = C Find Square Root
k = 35 In This Situation, k is C
3. A photograph is 40 cm long and 20 cm wide. Find its area.
Answer:
Area = 40×20
=800Step-by-step explanation:
Find the lateral area of a regular square pyramid if the base edges are of length 12 and the perpendicular height is 8.
Answer:
Lateral area of the pyramid = 120 square units
Step-by-step explanation:
In the figure attached,
A pyramid has been given with square base with edges of 12 units and perpendicular height as 8 units.
Lateral area of a pyramid = Area of the lateral sides
Area of one lateral side = [tex]\frac{1}{2}(\text{Base})(\text{Lateral height})[/tex]
= [tex]\frac{1}{2}(\frac{b}{2})(\sqrt{(\frac{b}{2})^2+h^2})[/tex] [Since l = [tex]\sqrt{r^{2}+h^{2}}[/tex]]
= [tex]\frac{1}{2}(6)(\sqrt{6^2+8^2})[/tex]
= [tex]3\sqrt{100}[/tex]
= 30 units²
Now lateral area of the pyramid = 4 × 30 = 120 square units
Answer: 240 units^2
Step-by-step explanation:
LA= 1/2 Pl
P= perimeter of base
l= lateral height
l= 8^2 + (12/2)^2 = 10^2
P= 12 x 4 = 48
48 x 10 = 480
480/2 = 240
240 units^2
If the ratio of red hairbands to green hair bands is 5 to 9 with a total of 70 hairbands, how many of them are green?
Answer:
45
Step-by-step explanation:
This can be written as 5r:9g. Add 5 and 9 to get the total of 14. You can write a ratio of 9 green: (out of) 14 total = x green: (out of) 70 total. Multiply 9 and 14 by 7 to get 45:70. Therefore, if there are 70 hairbands, 45 are green.
The weights of beagles have a mean of 25 pounds and a standard deviation of 3 pounds. A random sample of 50 beagles is collected. What is the probability that a sample of this size has a mean weight below 26 pounds?
Answer:
[tex] z =\frac{26-25}{\frac{3}{\sqrt{50}}}= 2.357[/tex]
And we can find the probability using the normal distribution table and we got:
[tex] P(z<2.357) =0.9908[/tex]
Step-by-step explanation:
Let X the random variable of interest and we can find the parameters:
[tex] \mu =25, \sigma= 3[/tex]
And for this case we select a sample size n =50. And since the sample size is higher than 30 we can use the central limit theorem and the distribution for the sample mean would be given by:
[tex] \bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
We want to find the following probability:
[tex] P(\bar X <26)[/tex]
And we can use the z score formula given by:
[tex] z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] z =\frac{26-25}{\frac{3}{\sqrt{50}}}= 2.357[/tex]
And we can find the probability using the normal distribution table and we got:
[tex] P(z<2.357) =0.9908[/tex]
College students were given three choices of pizza toppings and asked to choose one favorite Results are shown in the table toppings Sremam 15 24 28 28 15 1 11 23 28 cheese meat 23 15 veggie Estimate the probability that a randomly selected student who is a junior or senior prefers veggie. Round the answer to the nearest thousandth
A. 371
B. 220
C. 395
D. 662
Answer:
B. 0.220
Step-by-step explanation:
The table is presented properly below:
[tex]\left|\begin{array}{c|cccc|c}$toppings&$Freshman&$Sophomore&$Junior&$Senior&$Total\\---&---&---&---&---&---\\$Cheese&11&15&24&28&78\\$Meat&23&28&15&11&77\\$Veggie&15&11&23&28&77\\---&---&---&---&---&---\\$Total&&&&&232\end{array}\right|[/tex]
Number of junior students who prefers veggies =23
Number of senior students who prefers veggies =28
Total =23+28=51
Therefore, the probability that a randomly selected student who is a junior or senior prefers veggie
=51/232
=0.220 (to the nearest thousandth)
The correct option is B.
Keiko sold 3 less than three-fourths of his sister’s sales. Which expression represents what Keiko sold?
3/4x - 3
3/4x + 3
3x + 3/4
3x - 3/4
[tex]\frac{3}{4} x-3[/tex]
An algebraic expression is an expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.
Three-fourths is denoted by [tex]\frac{3}{4} [/tex]
Let sales of Keiko's sister be [tex]x[/tex]
Also, Keiko sold [tex]3[/tex] less than three-fourths of his sister’s sales.
So, an expression that represents what Keiko sold is given by [tex]\frac{3}{4} x-3[/tex]
For more information:
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Wat is the greatest common factor of 20 and 36
Answer:
20=1,2,4,5,10,2036=1,2,3,4,6,9,36Answer:- 4Answer:
GCF = 4
Step-by-step explanation:
Factors of 20 = 1,2,4,5,10 and 20
Factors of 36 = 1,2,3,4,6,9,12,18 and 36
Greatest factor which is common = 4
If f(x) = 4x – 8 and g(x) = 5x + 6, find (f - g)(x).
Answer:
(f - g)(x) = -x - 14
Step-by-step explanation:
Step 1: Plug in equations
4x - 8 - (5x + 6)
Step 2; Distribute negative
4x - 8 - 5x - 6
Step 3: Combine like terms
-x - 14
Answer:
-x-14
Step-by-step explanation:
Hope this helps
Which inequality is represented by the graph?
Answer:
y <= (2/5)x - 3/2
Step-by-step explanation:
y-intercept is -3/2
slope = 2/5
shading is below the line
Answer: y <= (2/5)x - 3/2
Find the perimeter of the following trapezoid:
6 ft
2.5 ft/ 12 ft
2.5 ft
8 ft
Answer:
31ft
Step-by-step explanation:
6 ft + 2.5 ft + 12 ft + 2.5 ft + 8 ft = 31ft
I assumed the slash in the space between 2.5ft and 12ft was an error, so I ignored it in the solution to this problem.
Besides that, perimeter is found by adding all sides of the shape or figure together, and the sum of that is the perimeter.
The basic formula for perimeter is:
base + height + base + height.
I do not think you square perimeter as you do area (e.g. 31ft^2).
A biologist samples and measures the length of the fish in a lake. What is the level of measurement of the data?
Answer:Ratio
Step-by-step explanation:
The ratio data because length has a true zero, and ratios of lengths are meaningful.
If the coefficient of realism alpha equals 1, then the criterion of realism will yield the same result as the maximax criterion.
A. True
B. False
Answer:
True
Step-by-step explanation:
Coefficient of realism called alpha which is a decimal number between 0 and 1. This number provides the optimistic view. The number 1 - [tex]\alpha[/tex] is amount of emphasis that is placed in pessimistic outcome. If the coefficient of realism alpha is 1 then criterion of realism will yield same result as maxi max criterion.
three night guard A, B and C blow their whistles at intervals of 8, 15 and 18 mins respectively, if they blow at 11.00pm, when next are they expected to blow together
Answer:
5:00 AM
Solution:
we will have to find the lowest common multiple of 8 , 5 and 18.
Since they blow their whistles once every 8/5/18 minutes.. you can imagine it as the multiplication table for these numbers. The number on which all three overlap, is the LCM and hence the amount of time after they will blow their whistles together.
The LCM is 360
therefore, the guards will blow their whistles together 360 minutes after 11:00pm
360 minutes = 6 hours
6 hours after 11: 5:00AM
Answer:
Hey!
Your answer is 5:00 am!
Step-by-step explanation:
1) Find the LCM of 8, 15, 18...360
2) 360 mins = 6 hours
3) 11:00 pm + 6 hours = 5:00 am
Hope this helps!
whats the answer ???? help dude
Answer:
C. 44 °
Step-by-step explanation:
Angles on a straight line add up to 180 degrees.
180 - 88 = 92
Angles in a triangle add up to 180 degrees.
y + y + 92 = 180
y + y = 88
2y = 88
y = 88/2
y = 44
Answer:
The answer is 46"
Step-by-step explanation:
A triangle is 180 degrees
so u already know one side
180"-88" is 92
then divide 92 by 2 which is 46
Answer: 46"
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.
n=7, x=3, p=0.65
Answer:
P(X = 3) = 0.1442
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
In this problem we have that:
[tex]n = 7, p = 0.65[/tex]
We have to find P(X = 3).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{7,3}.(0.65)^{3}.(0.35)^{4} = 0.1442[/tex]
How to read a ruler?
Answer:
Look at the numbers on the sides. If they are not spaced out very far, it's centimeters. If they are spaced out very far, it's inches
Step-by-step explanation:
this is how you read a ruler
Answer:
Start at 0
Step-by-step explanation:
Start at 0, then see how far the object goes.
- 4/9+7/12+- 3/8=how solve it
Answer:
-17/72
Step-by-step explanation:
-4/9 + 7/12 + (-3/8) =
We need a common denominator. The least common multiple of 9, 12, and 8 is 72.
= -4/9 * 8/8 + 7/12 * 6/6 + (-3/8) * 9/9
= -32/72 + 42/72 - 27/72
= 10/72 - 27/72
= -17/72
Answer:
Your correct answer is 17/72
Find an equation of the plane. The plane through the points (0, 7, 7), (7, 0, 7), and (7, 7, 0).
Answer:
x + y + z = 14
Step-by-step explanation:
If the points are designated A, B, C, then ...
AB × AC = (7, -7, 0) × (7, 0, -7) = (49, 49, 49).
That is, a vector perpendicular to the plane is (1, 1, 1), so the equation of the plane can be ...
(1, 1, 1)·(x, y, z) = (1, 1, 1)·A
x + y + z = 14
Marko drovev75mile in 1 1/2 hours .how many mile can he he drive in 1 hour
Answer: 50 miles
Step-by-step explanation:
75 miles in one and half hours.
That's 25 miles per half hour
So, in 1 hour, he will drive 50 miles
PLEASEE I NEED HELP!!
Determine whether each number is part of the solution set of x < 3.9.
x=41
Part of the Solution Set
Not Part of the Solution Set
x= -3.9
x= 3.9
x=4
x = 4,3
X=38
Answer:
Part of the solution set :
x = -3.9x = 3.9x = 3.8Not part of the solution set :
x = 4.1x = 4x = 4.3Step-by-step explanation:
Given that x must be smaller or equal to 3.9 .
So any number that is greater than 3.9 will not be part of the set of x.
CAN ANYONE HELP AT ALL? The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at $3, sales will reach 8000 Fun Noodles per day during the summer. Raising the price to $6 will cause the sales to fall to 5000 Fun Noodles per day. PREDICT THE NUMBER OF SALES IF PRICE IS $3.50. (it's not 6,000)
Answer:
7500
Step-by-step explanation:
At the price of $3, they will have 8000 sales. (3, 8000)
At the price of $6, they will have 5000 sales. (6, 5000)
You can use the information to create an equation. Use the points above to find a slope.
8000 - 5000 = 3000
3 - 6 = -3
3000/-3 = -1000
The slope is -1000.
Plug the slope into the point-slope equation along with one of the above points.
y - y₁ = m(x₁ - x)
y - 8000 = -1000(x - 3)
y - 8000 = -1000x + 3000
y = -1000x + 11000
Now that you have an equation, plug in the price into the x-value to find the number of sales you will get.
y = -1000x + 11000
y = -1000(3.50) + 11000
y = -3500 + 11000
y = 7500
You will have 7500 sales.
Answer:
7500
Step-by-step explanation:
3. A tunnel is 300 feet deep and makes an angle of 30° with the ground, as shown below.
30°
300 feet
Tunne
How long is the tunnel?
Answer:
173.20 ft
Step-by-step explanation:
[tex] \tan \: 30 \degree = \frac{length \: of \: tunnel}{depth \: of \: tunnel} \\ \\ \frac{1}{ \sqrt{3} } = \frac{length \: of \: tunnel}{300} \\ \\ length \: of \: tunnel \\ \\ = \frac{300}{ \sqrt{3} } \\ \\ = \frac{300 \sqrt{3} }{3} \\ \\ = 100 \sqrt{3} \\ \\ = 100 \times 1.7320 \\ \\ = 173.20 \: ft[/tex]
what is the answer?!?!??!
Answer:
Option D
Step-by-step explanation:
It forms a linear pair (Angles on a straight line) with one of the interior angles of the triangle.
Answer:
D
Step-by-step explanation:
A linear pair of angles is when two angles add up to 180 degrees on a line.
Interior angles and exterior angles form a linear pair.
The solid below is made from 1 centimeter cubes. Find the total surface area of the solid. Be sure to include the correct unit in your answer.
Answer:
62 [tex]cm^{2}[/tex]
Step-by-step explanation:
A 1 centimetre cube implies that its length = width = height = 1 cm.
Thus, the area of a surface of the cube = length × length
= 1 × 1
= 1 [tex]cm^{2}[/tex]
Considering the views or parts of the given solid;
Surface area of its left side = Surface area of its right side = 1 × 10
= 10 [tex]cm^{2}[/tex]
Surface area of the front elevation = Surface area of its back = 1 × 9
= 9 [tex]cm^{2}[/tex]
Surface area of its plan = Surface area of its bottom = 1 × 12
= 12 [tex]cm^{2}[/tex]
Total surface area of the solid = 10 + 10 + 9 + 9 + 12 + 12
= 62 [tex]cm^{2}[/tex]
The total surface area of the solid is 62 [tex]cm^{2}[/tex].
An automobile manufacturer has given its van a 47.2 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 250 vans, they found a mean MPG of 47.0. Assume the population standard deviation is known to be 1.9. A level of significance of 0.02 will be used.
A. Find the value of the test statistic.
B. State the null and alternative hypotheses.
Answer:
A
The test statistics is [tex]t = -1.7[/tex]
B
The Null and Alternative hypothesis are
[tex]H_o : \mu = 47.2[/tex] and [tex]H_a : \mu \ne 47.2[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 47.2 miles/gallon(MPG)[/tex]
The sample size is [tex]n = 250 \ van[/tex]
The sample mean is [tex]\= x = 47.0[/tex]
The sample standard deviation is [tex]\sigma = 1.9[/tex]
The level of significance is [tex]\alpha = 0.02[/tex]
Given that the value which the manufacturer gave the automobile is 47.2 and it is believed that this is not correct, then
The Null Hypothesis is
[tex]H_o : \mu = 47.2[/tex]
The alternative Hypothesis is
[tex]H_a : \mu \ne 47.2[/tex]
The test statistics can be mathematically evaluated as
[tex]t = \frac{\= x- \mu}{\frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{\= 47- 47.2}{\frac{1.9 }{\sqrt{250} } }[/tex]
[tex]t = -1.7[/tex]
30 POINTS IF ANSWERED IN THE NEXT FIVE MINUTES. Ms. Roth has made 200 headbands and is deciding what price to charge for them. She knows that she will sell more if the price is lower. To estimate the number she can expect to sell, she uses the function defined as ()=200−1.5, where is the price in dollars. Which choice describes a function, (), that models the total sales in dollars she can expect?
Answer:
198.5
Step-by-step explanation:
() = 200 - 1.5
() = 198.5
im not sure if this is what you are asking, but i hope it helps
Answer:
S=p(200-1.5)