Using traditional methods it takes 8.5 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 21 students and observed that they had a mean of 8.8 hours with a variance of 1.21 . Is there evidence at the 0.05 level that the technique performs differently than the traditional method? Assume the population distribution is approximately normal. Step 1 of 5 : State the null and alternative hypotheses
Answers
As the p-value of the test is of 0.215 > 0.05, there is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.
What are the null and the alternative hypothesis?At the null hypothesis, it is tested if there is no evidence of different performance, that is, the mean is of 8.5 hours, hence:
[tex]H_0: \mu = 8.5[/tex]
At the alternative hypothesis, it is tested if there is evidence of different performance, with a mean different of 8.5 hours, hence:
[tex]H_1: \mu \neq 8.5[/tex]
What is the test statistic?The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.
The equation is given as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters for this problem are given as follows:
[tex]\overline{x} = 8.8, \mu = 8.5, \sigma = \sqrt{1.21} = 1.1, n = 21[/tex]
Hence the test statistic is calculated as follows:
[tex]z = \frac{8.8 - 8.5}{\frac{1.1}{\sqrt{21}}}[/tex]
z = (8.8 - 8.5)/(1.11/square root of 21)
z = 1.24.
What is the p-value and conclusion?The p-value is obtained using a z-distribution calculator.
We have a two-tailed test, as we are testing if the mean is different of a value, with a test statistic of z = 1.24, hence the p-value is of:
0.215.
(2 multiplied by the subtraction of one and the p-value of z = 1.24).
The p-value is greater than the significance level of 0.05, meaning that there is not enough evidence to reject the null hypothesis and conclude that there is a difference between the two methods.
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Related Questions
Compare the two linear functions listen below
Answers
The slopes of function 1 and function 2 are respectively; -4 and 2. Thus, function 1 has a negative slope
How to find the slope of a linear function?The slope is simply defined as the change in the y-values divided by corresponding change in x-values.
1) Now, the formula for the slope between two coordinates is;
Slope = (y₂ - y₁)/(x₂ - x₁)
Let us take two coordinates from the table as;
(0, 50) and (1, 46). Thus;
Slope = (46 - 50)/(1 - 0)
Slope = -4
2) The general equation for equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, we are given the equation as;
c = 2d + 10
Comparing to the standard form, we have;
Slope = 2
Thus, function 1 has a negative slope
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Mr.martland decides the length of his square vegetable garden will be 17 ft. He calculates that the area of the garden is 34 ft^2. is he correct?
Answers
Answer:
Nope
Step-by-step explanation:
If it is a square garden, all sides are equal. Area would be 17x17 and that would equal [tex]289^{2} ft[/tex] not 34
A group of friends wants to go to the amusement park. They have no more than $90 to spend on parking and admission. Parking is $16.50, and tickets cost $10.50 per person, including tax. Use the drop-down menu below to write an inequality representing pp, the number of people who can go to the amusement park.
Answers
The inequality representing p, the number of people who can go to the amusement park, is given as follows:
10.5p + 16.5 ≤ 90.
How to build the inequality?The inequality for this problem is build considering the linear cost function, defined in slope-intercept format as follows:
C(p) = mp + b.
In which the parameters are given as follows:
m is the slope, representing the cost of the ticket per person.b is the intercept, representing the cost of parking.Parking is $16.50, and tickets cost $10.50 per person, hence the numeric values of the slope and the intercept are given as follows:
m = 10.50, b = 16.50.
Thus the cost function is given as follows:
C(p) = 10.5p + 16.5.
They have no more than $90 to spend on parking and admission, hence the inequality is defined as follows:
C(p) ≤ 90.
10.5p + 16.5 ≤ 90.
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help ill give brainiest <3 dont guess
Answers
Answer:
rectangular prism, 6 faces, 8 vertices
Answer:
The figure is a rectangular prism with 6 faces, moreover, it has 8 vertices.
3x + 2y = 5
x = 2y + 7
Answers
Answer:
I hope this helps you...
please mark me as brainliest..
The Burj Khalifa building in Dubai, United Arab Emirates, is one of the tallest buildings in the world at 2,722 feet tall. An American football field is 360 feet in length. Approximately how many football fields tall is the Buri Khalifa building? Round to the nearest tenth.
Answers
Answer:
7.5 which rounds to 8
Step-by-step explanation:
2,722 divided by 360 equals 7.56
check if needed <3
A car is traveling at a speed of 61 kilometers per hour. What is the car's speed in kilometers per minute? How many kilometers will the car travel in 20 minutes? Do not round your answers.
Answers
The car's speed in kilometers per minute is 1.01667. And the number of kilometers will the car travel in 20 minutes will be 20.33 kilometers.
What is speed?Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Time
A car is traveling at a speed of 61 kilometers per hour.
Convert the speed into a kilometer per minute. Then we have
Speed = 61 / 60
Speed = 1.01667 kilometers per minute
Then the number of kilometers will the car travel in 20 minutes will be given as,
1.01667 = d / 20
d = 1.01667 x 20
d = 20.33 kilometers
The car's speed in kilometers per minute is 1.01667. And the number of kilometers will the car travel in 20 minutes will be 20.33 kilometers.
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`y=7/(1,000)-(9x)/8` whats the y incercept
Answers
Please help me due in 1 hour, i'll give 5 stars and lots of points.
this table shows how many males and females attended two different movies.
Answers
Answer:
B
Step-by-step explanation:
Someone help plz make sure it’s right plz will mark brainiest
Answers
Answer:
Your answer is B, or the second one from the left
Answer: It would be the 2nd choice
Which is a recursive formula for the sequence 99. 4, 0, –99. 4, –198. 8, where f(1) = 99. 4? f(n 1) = f(n) 99. 4, n ≥ 1 f(n 1) = f(n) – 99. 4, n ≥ 1 f(n 1) = 99. 4f(n), n ≥ 1 f(n 1) = –99. 4f(n), n ≥ 1
Answers
A recursive formula for the sequence is: f(n+1) = f(n)-99.4, n ≥ 1
Consider the given sequence.
99.4, 0, -99.4, -198.8, . . .
We can observe that each next term of the sequence is decreased by -99.4
i.e., f(0) = 99.4
f(1) = f(0) - 99.4
f(1) = 99.4 - 99.4
f(1) = 0
f(2) = f(1) - 99.4
f(2) = 0 - 99.4
f(2) = -99.4
From these calculations we can say that the n-th term would be,
f(n) = f(n - 1) - 99.4
Therefore, recursive formula: f(n+1) = f(n) - 99.4
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if 2/3 x - 1=4, then x =?
Answers
or
x = 7 1/2
What are the roots of the equation x² - 10x +34 = 0 in simplest
a + bi form?
Answers
x = (10 +/- sqrt(10^2 - 4134)) / (2*1)
This simplifies to:
x = (10 +/- sqrt(100 - 136)) / 2
The square root of a negative number is equal to a complex number in the form a + bi, where a and b are real numbers and i is the square root of -1. Therefore, the roots of the equation x^2 - 10x + 34 = 0 are:
x = (-10 + sqrt(-36)) / 2 = (-5 + 3i) / 2 = -2.5 + 1.5i
x = (-10 - sqrt(-36)) / 2 = (-5 - 3i) / 2 = -2.5 - 1.5i
In simplest a + bi form, the roots of the equation are -2.5 + 1.5i and -2.5 - 1.5i.
PLEASE HELP 10 POINTS
Answers
Answer:
9.75
Step-by-step explanation:
3/4 |1/3x+2| < 6
you can turn the < into a =
then subtract 3/4 from 6 which leaves you with 5.25. And since you know 2 will always be positive because it's in an absolute value bracket 5.25-2=3.25. Which leaves you with
|1/3x| = 3.25
then do 3.25/(1/3) which leaves you with 9.75
:)
The owner of a mall retaurant bought 75 kilogram of rice. Each week, the retaurant ue 4. 5 kilogram of rice. Function r give the remaining amount of rice, in kilogram, a a function of the number of week ince the retaurant owner bought the rice. 1. Complete the table. Clear All
Answers
function f(x) = 75 - 4.5 w.
where w = number of weeks.
this question is related to function and solution is as follows,
The owner of a mall Restaurant bought rice = 75 kg
Each week, the restaurant use rice = 4. 5 kg
so we have to make an equation of function by which we can find out the remaining rice after w number of weeks,
f(x) = 75 - 4.5 w
where ,w = number of weeks
example, find out rice after 6 weeks
number of weeks (w) = 6
put it in the function,
f(x) = 75 - 4.5(6)
f(x) = 75 - 27
f(x) = 48.
so the function is ,f(x) = 75 - 4.5 w.
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Carmen uses 2/7 of a bag of flour to make 1/2 of a batch of her special homemade cookies. How many bags of flour does it take to make 3 batches of the cookies?
Answers
Answer:
12/7 or 1 5/7
Step-by-step explanation:
2/7=1/2, so 4/7=1. multiply 4 by three, since one times three equals three.
Make a tree diagram to show sample space. Then select the total number of outcomes.
choosing black, blue or brown socks with boots, gym shoes or dress shoes
a. 3
C. 9
b. 6.
d. 12
PLEASE HELP
Answers
Answer:
C. 9
Step-by-step explanation:
3 sock options, 3 shoe options for each of those sock options.
3 x 3 = 9
Find the missing length. Round to the nearest tenth.
HELP PLEASE!!
Answers
Use the Pythagorean theorem
3^2 + 7^2 = c^2
9 + 49 = 58
square root of 58 =
7.615
Find the measure of the indicated angle. Need help please.
I need explanation too
PLEASE NO LINKS I WILL REPORT YOU
Answers
Answer:
AC=35
Step-by-step explanation:
Sin=opposite/hypotenuse
Sin54=AC/43
AC=43sin54
AC=34.78≈35
Order these numbers from least to greatest.
6.1031, 6.203, 6.1, 6.23
Answers
Answer:
6.2300, 6.2030, 6.1031, 6.1000
Step-by-step explanation:
Answer:
6.1, 6.1031, 6.203, 6.23
Some fireworks are fired vertically into the air from the ground at an initial speed of 80 feet per second. The equation for this object's height h(t) at time t seconds after launch is h(t) = -16t2 + 80t. a. Find the vertex. Explain what this means in the context of the situation
Answers
Answer:
Vertex (-2.5,-300)
Step-by-step explanation:
We are given with h(t)=-16 t^2 +80 t. We are asked to find the vertex.
X-coordinate of vertex =[tex]\frac{-b}{2a}[/tex]
Where 'a' is coefficient of [tex]t^{2}[/tex] term
'b' is coefficient of 't' term.
From given function, a= -16
b=80
So,
x-coordinate of vertex =[tex]\frac{-80}{2(-16)}[/tex]
=-2.5
y-coordinate of vertex =[tex]-16(-2.5)^{2} +80(-2.5)[/tex]
Simplify it,
=-100 -200
= -300
So, vertex is at (-2.5, -300).
david mowed 2/3 of the yard in 1/2 hour how long will it take him to mow the whole yard?
Answers
Answer:
Step-by-step explanation: It would take him 15 minutes more to mow the whole yard
1/2 hour is 30 mins divided by 2 which is 15 mines times 3 is 45 mins total mins
Will give brainliest if right
O C. 65
O D. 50
Answers
Answer:
D
Step-by-step explanation:
istg if one of yall roasts my dirty calculator
Math
On a grid, a middle school is located at ( − 5 , 3 ) , and a library is located at ( 2 , 3 ) . If 1 unit represents 1 mile on the grid, how far is the library from the middle school?
Answers
Answer:
14 miles
Step-by-step explanation:
there are 14 units in between point (-5,3) and (2,3), and since each unit is 1 mile it would be 14 miles.
convert 20% profit into profit amount
Answers
Answer: To convert 20% profit into a profit amount, you would multiply 20% by the revenue or cost of the item or service.
Let's say,
You have revenue of $1000
So,
20/100 * 1000 = $200
So the 20% profit on the revenue of $1000 is $200.
It's important to note that profit is the amount of money you make after you subtract your costs from your revenue. It's the amount you have left after all the expenses, taxes and other deductions are made.
Step-by-step explanation:
What is the explanation please help me
Answers
Answer:
Yes. If the first friend descended 0.11 mile (-0.11) and the second friend descended 0.12 mile (-0.12), then the second friend had to have caught up to the first friend knowing that the second friend descended at least 0.11 mile. Hope this helps :)
Step-by-step explanation:
Question 1
Find the distance: Speed = 99 km/h,
Time = 40 mins
Answers
Distance = 99 x 40
Distance = 3,960
Answer:
40 minute = 40 : 60 hours
= 4/6 [÷10]
= 2/3 [÷2]
distance = speed × time
distance = 99 kilometers/hours × 2/3 hours
distance = 33 × 2
distance = 66km
Order of operation help I have 4 min left on my timer . NO LINKS
Answers
Answer:
13
Step-by-step explanation:
Just In case you want explanation-
1. 4 squared Meaning 4 x 4 = 16
2. 16 x 6 = 96
3x 6 = 18
96- 18 = 78
in the denominator, 25/ 5 = 5
11 minus 5 = 6
78 divided by 6
it gives you 13
Answer:
13
Step-by-step explanation:
Order of operations:
Parenthesis, exponents, multiplication and division, addition and subtraction
Solve for x. Leave your answer in simplest radical form.
15 in
X
Answers
Answer:
√124
Step-by-step explanation:
a^2+b^2=c^2
x^2+101= 225
x^2= 225-101
x^2= √124
What does 4 mean in maths?
Answers
The meaning of the 4! ( factorial ) in mathematics is equal to ( 4 × 3 × 2 × 1 ).
As given in the question,
Given expression in mathematics is written as :
4! ( factorial )
In standard form meaning of the n! ( factorial ) is given by multiplication of all the terms in decreasing order till 1.
It is expressed as:
n! = n × ( n - 1 ) × ( n - 2 ) × ( n - 3 ) × ........× 3 × 2 × (n - (n - 1) ).
Apply this formula for 4! ( factorial ) we get,
4! ( factorial )
= 4 × ( 4 - 1 ) × ( 4 - 2 ) ×( 4 - 3)
= 4 × 3 × 2 × 1
= 12
Therefore, the meaning of 4! ( factorial ) in mathematics is given by
4 × 3 × 2 × 1 .
The above question is incomplete , the complete question is :
What does 4! ( factorial ) mean in mathematics?
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