A student believes that the average grade on the statistics final examination was 87. A sample of 36 final examinations was taken. The average grade in the sample was 83.96 with a standard deviation of 12. The student wants to test whether the average is different from 87 at 90% level of confidence. Compute the p-value for this test.
Answer:
The p-value for this test is 0.1375.
Step-by-step explanation:
A student believes that the average grade on the statistics final examination was 87. The student wants to test whether the average is different from 87 at 90% level of confidence.
At the null hypothesis, we test if the average is 87, that is:
[tex]H_0: \mu = 87[/tex]
At the alternate hypothesis, we test if the average is different from 87, that is:
[tex]H_a: \mu \neq 87[/tex]
The test statistic is:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
[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, [tex]s[/tex] is the standard deviation of the sample and n is the size of the sample.
87 is tested at the null hypothesis:
This means that [tex]\mu = 87[/tex]
The average grade in the sample was 83.96 with a standard deviation of 12. Sample of 36
This means that [tex]X = 83.96, s = 12, n = 36[/tex]
Value of the test-statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{83.96 - 87}{\frac{12}{\sqrt{36}}}[/tex]
[tex]t = -1.52[/tex]
Pvalue:
Probability of the sample mean differing of 87, which means that we have a two-tailed test, with t = -1.52 and 36 - 1 = 35 degrees of freedom.
With the help of a calculator, the pvalue is of 0.1375.
The p-value for this test is 0.1375.
You are walking near a river. While standing at A, you measure an angle of 90° between B and C, as shown. You then walk to B and measure
an angle of 61° between A and C. The distance between A and B is about 1 mile. How wide (in miles) is the river between A and C? Round your
answer to the nearest tenth.
61
B Im
A
The width is about
miles.
Answer:
3.6
Step-by-step explanation:
tan61=x/2
2(tan61)=x
3.6=x
Need help plz!?!?!?!?!?!
Answer:
113
Step-by-step explanation:
The volume of a sphere is [tex]\frac{4}{3}\pi r^3[/tex], where [tex]r[/tex] is the radius of the sphere. The radius of the given sphere is 3 ft, so its volume is [tex]\frac{4}{3} \pi \cdot 3^3 = 36\pi[/tex]. Using 3.14 for [tex]\pi[/tex], this is approximately equal to 113.04. Rounding to the nearest whole number, the answer is 113 cubic feet.
Answer: 113 (rounded)
Step-by-step explanation:
Hey!
So for this we just use our sphere formula and follow the steps.
Volume= 4/3 πr^3
R= radius (half of diameter)
For pi we are going to use 3.14.
Let’s work this out now.
Radius is 3 so since it is cubed, we multiply it by itself 3 times. We get 27. Now, let’s multiply this by 3.14 and get 84.78.
Lastly, multiply by 4/3. We get 112.9333. This is the volume.
Hope this helped! :D
Sorry I messed any thing up!
Comment down below for further questions!
ABCD is a rectangle with BC =63 and AB = 84. Find each measure.
tell me all the questions of this
Answer:
To find the radius..just divide them by two
For the diameter multiply by two
Circumference formula is
[tex]2\pi \: r[/tex]
What is the measure of c?
Answer:
45 degrees
Step-by-step explanation:
The Students' Union needs to order some pens and notebooks. How much does it cost to order 1000 pens and 2000 notebooks?
$
Pen
Quantity 100 250 500 1000 2500 5000
Price per pen (cents) 80c 72c 66c 60c 52c 45c
Notebook
Quantity 100 250 500 1000 2500 5000
Price per notebook (cents) 99c 86c 80c 76c 72c 70c
The cost to order 1, 000 pens and 2, 000 notebooks, by the Student Union, can be found to be
How to find the cost of ordering the pens and notebooks ?The cost of ordering 1, 000 pens is shown to be 60 cents per pen so the total cost would be :
= Number of pens x Cost per pen
= 1, 000 x 60 cents
= $ 600
The cost of ordering 2, 000 notebooks is 76 cents per notebook which comes to a total of :
= 2, 000 x 76 cents
= $ 1, 520
The total cost of ordering the pens and notebooks is:
= 600 + 1, 520
= $ 2, 120
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I need help in this with explanation
Step-by-step explanation:
The figure is made up of an 8x8 square and 4 identical triangles with 8-ft bases and 4 ft in height. Each triangle has an area = (1/2)bh = (1/2)(8)(4) = 16 ft^2. The square part has an area of 8x8 = 64 ft^2. Therefore, the total area of the figure is
A = (area of square) + 4×(area of triangle)
= 64 ft^2 + 4(16ft^2)
= 128 sq ft
Find the sum and express it in simplest form.
(-7n² - 8n - 8) + (-n² + 9n + 9)
008
Clear all
Enter the correct answer.
+ BO
DONE
The simplest form of the given expression is (- 8n² +n +1)
What is simplification?Simplification is the process of making simple an expression, terms or equations so as to easy for solving or evaluating.
There are some steps for simplification such as removing parenthesis, collecting like terms, addition or subtraction of like terms and so on.
How to find the sum and express in simplest form?We are given an expression, ( -7n² - 8n -8) + (- n² + 9n +9)
In order to simplify, we first remove the parenthesis and get
- 7n² - 8n -8 - n² + 9n +9
in the next we will collect like terms
- 7n² - n² -8n +9n - 8 +9
We now add or subtract like terms
- 8n² + n+1
this is the simplest form of the given expression.
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Kisha bought a pair of shoes originally marked $48.35. The
salesclerk told her she would get a 20% discount. How much
money did she save?
$38.68
$9.67
$8.83
$38.35
Answer:
she saved $9.67
Step-by-step explanation:
$48.35÷ 0.20= $9.67
B) If one gallon of paint covers 0.5 square meters, how many gallons of black paint wil they
need to paint the house?
Show your work
1
Answer:
depends on the size of the house
let's say the house is 10 square meter then you would need 5 gallons
let's the house is 60 square meter then you would need 30 gallons
Step-by-step explanation:
whatever the square meter just divide it with 2 and that should be your answer
After standardizing a NaOH solution, you use it to titrate an HCl solution known to have a concentration of 0.205 M. You perform five titrations and obtain the following results: 0.213, 0.204, 0.208, 0.200, and 0.198 M.
a) What is the mean?
b) What is the standard deviation of mean?
Answer:
The right answer is:
(a) 0.205
(b) 0.005425
Step-by-step explanation:
The given data is:
0.213, 0.204, 0.208, 0.200, and 0.198
(a)
The mean will be:
= [tex]\frac{Sum \ of \ all \ data}{No. \ of \ data}[/tex]
= [tex]\frac{0.213+ 0.204+ 0.208+ 0.200+0.198}{5}[/tex]
= [tex]\frac{1.023}{5}[/tex]
= [tex]0.2046[/tex]
or,
= [tex]0.205[/tex]
(b)
The standard deviation will be:
[tex]\sigma^2=\Sigma\frac{(x_i-\mu)^2}{N}[/tex]
[tex]=\frac{(0.213-0.2046)^2+...+(0.198-0.2046)^2}{5}[/tex]
[tex]=\frac{0.0001472}{5}[/tex]
[tex]=2.994\times 10^{-5}[/tex]
or,
[tex]=0.005425[/tex]
find the area of the polygon.
Answer:
174 ft²
Step-by-step explanation:
The polygon cam be decomposed into two rectangles.
The area of the polygon = rectangle A + rectangle B
Area of rectangle A = L* W
L = 18 ft
W = 9 ft
Area of rectangle A = 18*9 = 162 ft²
Area of rectangle B = L* W
L = 20 - 18 = 2 ft
W = 6 ft
Area of rectangle A = 2*6 = 12 ft²
✔️Area of the polygon = 162 + 12 = 174 ft²
A study conducted on 40,000 words in the English language found that about 6,670 words started with the letter T, which Is the most common
letter to start a word. If we randomly pick of 20 unique words, which of these lists of words will come closest to the theoretical probability of getting
a word beginning with T?
Answer:
To answer this problem, first let us calculate for the theoretical probability obtained from the study conducted:
Theoretical Probability = 6,670 / 40,000
Theoretical Probability = 0.16675 = 0.17
From the given choices, the list of words which can give this similar amount of probability is:
“to, sarcastic, epithet, for, less, corruptible, than, the, offspring, open, any, primary, loyalty, table, out, whom, example, who, mention, say”
In this set of words, the number of words starting with letter T is 4. Calculating for the probability of getting a word starting with T in this set is:
Sample probability = 4 / 20
Sample probability = 0.20
Step-by-step explanation:
Could someone help answer this? Thanks!
The limit of a function y=f(x) at x=a is sometimes best understood as the approximate height of the function around x=a based on the values around x=a whereas the value of the function f at x=a is the exact height of the function at that point. Consider two functions 1) f(x)=x+1 and g(x)=(x^2-1)/(x-1). Answer the following questions. (a) Discuss the process of finding the limit x->1 f(x). (b) How does it differ from f(1)?
a) The process to find the limit is given as follows:
f(x): simply replace x by 1.g(x): factor and then replacing.b) When a function does not have any discontinuity at x = 1, the procedure is the same as calculating f(1), however in the case of a discontinuity, such as for f(x), the discontinuity first has to be removed, if possible.
How to calculate the limit of a function?The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.
Hence:
lim x -> 1 f(x) = 1 + 1 = 2.lim x -> 1 g(x) = (1² - 1)/(1 - 1) = 0/0.For the case of g(x), there is a discontinuity, meaning that the function has to be factored to remove the discontinuity.
Applying the subtraction of perfect squares, we have that:
x² - 1 = (x - 1)(x + 1).
Then:
g(x) = (x - 1)(x + 1)/(x - 1) = x + 1.
Meaning that the limit is then calculated as follows:
lim x -> 1 g(x) = lim x->1 x + 1 = 1 + 1 = 2.
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80 POINTS This is a picture of Joseph Stalin, Franklin Roosevelt, and Winston Churchill at the Tehran Conference in 1943. They were the leaders of the Soviet Union, the United States, and the United Kingdom. During World War II, these men were known as the "Big Three" because they led
A.
the most powerful of the Allied countries.
B.
countries that had declared war on each other.
C.
the countries that suffered the most casualties in the war.
D.
the only countries fighting against Nazi Germany.
Option A. They led the most powerful of the Allied countries.
Nathan invested $80,000 in an account paying an interest rate of 6% compounded
continuously. Assuming no deposits or withdrawals are made, how long would it
take, to the nearest year, for the value of the account to reach $175,600?
Answer:
Number of year = 13 year and 6 month approx.
Step-by-step explanation:
Given:
Amount invested = $80,000
Rate of interest = 6% compounded continuously
Future value of investment = $175,600
Find:
Number of year
Computation:
Future value of investment = Amount invested[1 + Rate of interest]ⁿ
175,600 = 80,000[1+6%]ⁿ
175,600 = 80,000[1+0.06]ⁿ
175,600 = 80,000[1.06]ⁿ
Number of year = 13.492 year
Number of year = 13 year and 6 month approx.
Please help me on this question
Answer:
Your answer is A
Step-by-step explanation:
A = pi*r²
A = 3.14*70²
A = 3.14*4900
A = 15386
The questions on a multiple choice test have four answer choices.
Which of the following models could you use to simulate the outcome of guessing the correct answers to a 50-question test?
(HINT: Remember to choose a model with the same number of possible outcomes as each test question.)
Group of answer choices
A. flipping a coin 50 times
B. spinning a spinner with 4 equal sections 50 times
C. rolling a 6-sided die 50 times
D. spinning a spinner with 50 equal sections four times
Answer: spinning a spinner with 4 equal sections 50 times
Step-by-step explanation:
The models that one can use to simulate the outcome of guessing the correct answers to a 50-question test will be to spinn a spinner with 4 equal sections 50 times.
Flipping a coin 50 times is wrong since the coin only has two outcomes which are head and tail. Rolling a 6-sided die 50 times is also wrong.
Therefore, the correct option is B.
A line passes through the point (4,-7) and has a slope of -1/2.
Click “show your work” below and show work to write the equation of the line in point-slope form.
Answer:
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
Slope "m"
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~~~~
( 4 , - 7 )
m = [tex]-\frac{1}{2}[/tex]
y - ( - 7 ) = [tex]-\frac{1}{2}[/tex] ( x - 4 )
y + 7 = [tex]-\frac{1}{2}[/tex] ( x - 4 )
A machinist must cut 12 strips of metal that are each 3 ft 4 7/8 in. long. What is the total length needed in inches?
The total length needed in inches will be 490.5 inches.
How to calculate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Since the machinist must cut 12 strips of metal that are each 3 ft 4 7/8 in. long The total length needed in inches will be:
= (3 ft 4 7/8 inch × 12)
Note that 1 feet = 12 inches
= (12 × 3) + (4 7/8) × 12
= (36 + 4.875) × 12
= 490.5 inches
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The Board of Education (DOE) claims that the average salary of substitute teachers in school
district in Nassau County, NY, is about $175 per day. A random sample of 6 school districts is
selected, and the daily salaries (in dollars) are collected into calculation with sample mean is $80
and sample standard deviation is 6.3. Calculate at α = .05 significance level whether the true
mean greater than $175.
Please explain step by step and as clear as possible
The null hypothesis is rejected.
The mean is not greater than $175.
What is the hypothesis?An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.
Given:
Sample size (n) = 6
Sample mean ([tex]\bar x[/tex]) = $80
Sample standard deviation(s)=6.3
Significance level(α)=0.05
We have to test the claim that the true mean greater than $175.
The null and alternative hypotheses:
H₀ : μ = 175
H₁ : μ > 175
Here, Population Standard deviation is unknown and sample size is less than 30.
So we will use t- distribution.
Test Statistic t,
t = ([tex]\bar x[/tex] - μ) / {s/√n}
t = (80−175) / (6.3 /√6)
t = (80−175) / (6.3 / 2.45)
t = − 95 / 2.57196423
t = −36.937
degree of freedom (df) = n−1
= 6−1
= 5
p-value at t = −36.937, df = 5 and α = 0.05
Absolute value of −36.937 = 36.937
Notice that 36.937 does not show up in the table, but it does fall between the two values 31.821 and 63.657.
So, p-value = 1
Since, p-value > α
That means, we fail to reject the null hypothesis (H₀).
Therefore, the true mean is not greater than $175.
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If a 2 centimeter cube is placed inside a box that is 9 cm by 5 cm by 8cm ,
what is the volume inside the larger box that is outside of the smaller box?
DO NOT ANSWER IF YOU DO NOT KNOW THE ANSWER! Whoever answers correctly will get Brainliest! :)
Answer:
360 cm3
Step-by-step explanation:
Option d is the right answer
6 = z/4.5
please answer
Which function does not have a vertical asymptote
Answer:
[tex]y=\frac{5x}{1+2x^2}[/tex]
Step-by-step explanation:
[tex]Option ~A ~ does ~ not ~ have ~a ~ vertical~ asymptote[/tex]
--------------------------
Hope it helps...
Have a great day!!
Answer:
Step-by-step explanation:
answer is d
The water depth in a harbor rises and falls over time. The function f(t) = 4.1 sine (StartFraction pi Over 6 EndFraction t minus StartFraction pi over 3 EndFraction) + 19.7 models the water depth, in feet, after t hours.
During the first 24 hours, at what times does the water depth reach a maximum?
Answer:
Below
Step-by-step explanation:
f(t) = 4.1 (sin pi/6 t - pi/3) + 19.7 <===will be a maximum when the sin portion is equal to 1
so sin ( pi/6 t - pi/3) = 1 given that sin is equal to one at 0 and pi and 2 pi and 3 pi and 4 pi etc
pi/6 t - pi/3 = 0 or pi , 2 pi, 3 pi , 4 pi
then t = 2 and 8 and 14 and 20 hrs ( every 6 hrs starting with t = 2)
PLEASE HURRY I WILL GIVE BRAINLY PLEASE HURRY
In triangle LMN, m∠L = (4c + 53)°. If the exterior angle to ∠L measures 87°, determine the value of c.
c = 87
c = 8.5
c = 35
c = 10
Answer:c=35
Step-by-step explanation:
i just did this
244 is it
real number
rational number
irrational number
natural number
integer
Answer:
Step-by-step explanation:
It is a real number, a rational number, a natural number, and an integer.
Answer:
It’s a real number, rational number, and a natural number.
Find the area of the trapezoid
Answer:
20 is the answer
Step-by-step explanation:
I did the math.hope it helps :)
A table and 4 chairs costs N82. If the table costs N25, what is the cost of each chair? Find the total cost of 2 tables and 6 chairs
Answer:
Step-by-step explanation:buordjkdkeek