State the null hypothesis H0 and the alternative hypothesis Ha in each case. Be sure to identify the parameters that you use to state the hypotheses.
(a) A university gives credit in first-year calculus to students who pass a placement test. The mathematics department wants to know if students who get credit in this way differ in their success with second-year calculus. Scores in second-year calculus are scaled so the average each year is equivalent to a 75. This year 17students who took second-year calculus passed the placement test.
H0:μ>75;Ha:μ=75
H0:μ<75;Ha:μ=75
H0:μ=17;Ha:μ>17
H0:μ=17;Ha:μ≠17
(b) Experiments on learning in animals sometimes measure how long it takes a mouse to find its way through a maze. The mean time is 24 seconds for one particular maze. A researcher thinks that playing rap music will cause the mice to complete the maze slower. She measures how long each of 17 mice takes with the rap music as a stimulus.
H0:μ=24sec;Ha:μ>24sec
H0:μ=24sec;Ha:μ≠24sec
H0:μ>17sec;Ha:μ=17sec
H0:μ=17sec;Ha:μ<17sec
H0:μ=24sec;Ha:μ<24sec
(c) The average square footage of one-bedroom apartments in a new student-housing development is advertised to be 850 square feet. A student group thinks that the apartments are smaller than advertised. They hire an engineer to measure a sample of apartments to test their suspicion.
H0:μ=850ft2;Ha:μμ850ft2
H0:μ>850ft2;Ha:μ=850ft2
H0:μ=850ft2;Ha:μ>850ft2
H0:μ=850ft2;Ha:μ<850ft2
H0:μ<850ft2;Ha:μ=850ft2

Answers

Answer 1

Answer: (A)

[tex]H_0:\mu=75\\H_a:\mu\neq75[/tex]

(B)

[tex]H_0:\mu=24\ sec\\H_a:\mu>24\ sec[/tex]

(C)

[tex]H_0:\mu=850\ ft^2\\H_a:\mu<850 \ ft^2[/tex]

Step-by-step explanation:

Null hypothesis [tex](H_0)[/tex]: It is a statement showing population parameters as per the objective of the study. It generally takes "≤,≥,=" signs.  Alternative hypothesis [tex](H_a)[/tex]: It is also a statement describing population parameters as per the objective of the study. It generally takes ">, <, ≠" signs.

(A)  Objective: Scores in second-year calculus are scaled so the average each year is equivalent to a 75 or not.

[tex]H_0:\mu=75\\H_a:\mu\neq75[/tex]

(B) Objective: The mean time is 24 seconds or more for one particular maze.

[tex]H_0:\mu=24\ sec\\H_a:\mu>24\ sec[/tex]

(C) Objective: The average square footage of one-bedroom apartments in a new student-housing development is advertised to be 850 square feet or smaller.

[tex]H_0:\mu=850\ ft^2\\H_a:\mu<850 \ ft^2[/tex]


Related Questions

BRAINLIEST AND ACED+ PLEASE HELP ME :c

Answers

Answer:

1 1/2 x 4 1/2 x 5 =  33 3/4

Find two consecutive whole numbers that
82 lies between.

Answers

The question as written is incomplete, but square root of 82 is between the whole numbers 9 and 10, whose squares are 81 and 100 respectively.

Answer: The question as written is incomplete, but square root of 82 is between the whole numbers 9 and 10, whose squares are 81 and 100

Maths URGENT! I need answer rn

Answers

Answer:

8a-8c+6b

Step-by-step explanation:

3a-(-2c-5a)+6b-10c

3a+2c+5a+6b-10c

(3a+5a)+(2c-10c)+6b

8a-8c+6b

Pls HELP!!! Answer accurately... this should be very easy,

Answers

Answer:

85

Step-by-step explanation:

He has 170 correct answers, so 170 * 0.5 = 85 points  #0.5 points per 1 question

Mark went to the bookstore. He bought 3
books for $6.00 each and two magazines
for $3.50 each. He received a 25% discount
on his purchase. If he handed the cashier
$20, how much change did Mark get back?

Answers

Answer: $1.25

Step-by-step explanation: (6*3) = 18 + (2*3.50)= 7

18+7=25

25*.25= 6.25

25-6.25= 18.75

20-18.75 = 1.25

What is the area of the triangle?

Answers

Answer:

height ×base divided by two

What is the consequence of L'hopital's Rule?​

Answers

Answer:

So, L'Hospital's Rule tells us that if we have an indeterminate form 0/0 or ∞/∞ all we need to do is differentiate the numerator and differentiate the denominator and then take the limit. (Brainliest? :3)

Step-by-step explanation:

Respond Quick PLZ help me out determines if I fail

Answers

Answer:

1. infinite many solutions

2. With solution: x+y=7 ,2x+y=6

Without solution: x+y=8 ,x+y=9

Infinite solution: x+y=3, 2x+2y=6

Step-by-step explanation:

By the way, can you follow me?

Thanks!

Which value is NOT equivalent to the others
PLS HELP :(​

Answers

Answer:

Its 3 on top of 4

Answer:

The top right one

Step-by-step explanation:

4x4(2)

Simplify the expression and write your answer as a power
10

Answers

Answer:

10^88

Step-by-step explanation:

You have to multiply the exponents since they are in parenthesis.

Good Luck!

Answer:

The answer is C. 10^88

Step-by-step explanation

Whenever you have an exponent written like this, you must multiply the 8 and 11.  Which will give you 10^88.  I hope this has helped you!   :3    Sorry if it is incorrect.

3) Divide x3 + 4x2 – 3x – 12 by (x + 4)

Answers

Answer:

Factor the numerator and denominator and cancel out the common factors.

x ^2 − 3 is your final answer.

Step-by-step explanation:

Hope that this helps you out! :)  

If you have any questions please put them in the comment section below this answer.  

Have a great rest of your day/night!  

Please thank me on my profile if this answer has helped you.

no links plz help
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

the answer is essentially d

Decide whether the following statement is true or false. An infinite number of triangles can be created using the same three angle measures

Answers

Answer:

True

Step-by-step explanation:

I took the test!

Answer:

true is the answer

There are an infinite number of triangles which can be constructed with angles measuring this.

There are an infinite number of lengths the sides of the triangles can be while the angles stay the same measure.

Split the following into partial fractions.

1. x

(x+2)(x+3).

2. 11−3x

x2+2x−3

.

3. 2x

2−9x−35

(x+1)(x−2)(x+3).

4. x

3−2x

2−4x−4

x2+x−2

.

5. 2x+3

(x−2)3

.

6. 3+6x+4x

2−2x

3

x2(x2+3) .​

Answers

Answer:

Go on a calotor

Step-by-step explanation:

You can do this I know you can

Need help asap 10 points, provide explanation please.

Answers

Answer:

Step-by-step explanation:

Use the distance formula between points to find all sides:

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]

AB=[tex]\sqrt{13}[/tex]

BC=[tex]\sqrt{13}[/tex]

CA=[tex]\sqrt{26}[/tex]

This is a 45° 45° 90° triangle, where two of the sides are equal and the other side is the first two sides times [tex]\sqrt{2}[/tex], so yes, it is a right triangle.

Answer:

Answer D is correct.

Step-by-step explanation:

By inspection, the side lengths are {3, 4, 5}, and this triplet satisfies the Pythagorean Theorem:  3^2 + 4^2 = 5^2.  Thus this IS a right triangle.  

One could also find the lengths of the three sides using the distance formula and the endpoints of each line segment forming the triangle.

Answer D is correct.


Find how many quarts of 5% butterfat milk and 2% butterfat milk should be mixed to yield 45 quarts of 3% butterfat milk.
The mixture should contain quarts of the 5% butterfat milk.

Answers

Answer:

It would take 4 quarts of 5% buttermilk and 41 quarts of 2% buttermilk to make 45 quarts of 3% buttermilk.

Step-by-step explanation:

Let the number of 5% quarts = x

Let the number of 2% quarts = y

x+y=45

y=45-x

(.05)x+(.02)y=(0.03)45

5x+2y=102

5x+2(45-x)=102

5x+90-2x=102

3x=12

x=4

y=45-x=45-4=41

So it would take 4 quarts of 5% buttermilk and 41 quarts of 2% buttermilk to make 45 quarts of 3% buttermilk.

184 is what percent more than 148

Answers

it is 36 percent more

Find the area of the triangle

Answers

Answer:

[tex] \frac{4 \times 5}{2} = 10[/tex]

Becicy is renting a car for her vacation. The rental costs 5350 per week plus 20 cents per mile. If Becky can spend no more than $500,
how far can she travel

Answers

Answer:

750 miles

Step-by-step explanation:

Given that,

The rental costs 350 per week plus 20 cents per mile.

Becky can spend no more than $500.

Let he travel x miles. We can form an equation as follows :

350 + 0.2x = 500

0.2x = 500-350

0.2x = 150

x = 750 miles

Hence, she can travel 750 miles.

Liam invests $5,000 in an account that pays 2.5% compound interest annually. He uses the expression P(1+r)t to find the total value of the account after t years. What will be the total value of the account after 3 years?

Answers

Answer:

The final balance is $5,389.

The total compound interest is $389.

Step-by-step explanation:

2.) What is another way to write 700,562? Select all the ways to write this number, A) (7 +100,000) + (5+ 1,000) + (6 +10) + (2 +1) B) seven hundred thousand, five hundred sixty-two C) 700,000 +500 + 60 + 2 D) 7 hundred thousands +5 hundreds +62 tens. E) 7 hundred thousands +5 thousands + 6 tens + 2 ones​

Answers

Answer:

b,c

Step-by-step explanation:

b is written  in the written form properly and  is is extended using the right place values

PLEAES HELP 80 POINTS with branily I really need help and I will be forever in det to the person that helped me Bec this Is 40% of my grade And please don't steal my points I need them in doing a give away soon. :)
On the coordinate plane shown below, points
G and I have coordinates (6,4) and (3,2) , respectively.


1)Design a strategy in which the Pythagorean theorem is used to calculate the straight line distance between points
G and I

2) on a coordinate plane. Use complete sentences to describe the strategy.
Use the Pythagorean theorem to determine the distance between the two points on the coordinate plane. In your final answer, include all of your calculations.
Use the distance formula and the coordinates of points
G and I

3) to prove that the Pythagorean theorem is an alternative method for calculating the distance between points on a coordinate plane. In your final answer, include all of your calculations.

Answers

Answer:

sorry wanted pionts

Step-by-step explanation:

umm sorry

Answer: :Given : points G and I have coordinates (6,4) and (3,2)

To Find : Use  Pythagorean theorem  to calculate the straight line distance between points G and I

Solution:

points G and I have coordinates (6,4) and (3,2)

Draw a line parallel to y axis passing through G

Draw a line parallel to x axis passing through I

Intersection point K ( 6 , 2)

IK = 6 - 3 = 3

GK = 4 -2  = 2

ΔIKG right angled triangle

Pythagoras' theorem: square on the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two perpendicular sides.  

GI² = IK² + GK²

=>  GI²  = 3² + 2²

=>  GI²  = 13

=> GI = √13

using distance formula

G (6,4) and I (3,2)

= √(6 - 3)² + (4 - 2)²

= √3² + 2²

= √9 + 4

= √13

Learn More:

different approaches of Pythagoras theorem​ - Brainly.in

brainly.in/question/10516214

13. In Fig. 16.10, BCDE is a rectangle , ED = 3.88 cm,AD= 10 cm ...

brainly.in/question/19749562

a certain vehicle can drive 300miles on a tank of 20 gallons. how far can it drive on 30 gallons?

what is the answer in miles ??

PLEASE HELP ME !!!!

Answers

Answer:

450 miles

Step-by-step explanation:

First you calculate miles per gallon, which you do by dividing 300/20. This gives us 15. So you can go 14 miles on one gallon.

From there you multiply 15 by 30, since you'll be driving 30 miles. This gives us 450 miles.

Step-by-step explanation:

[tex] \frac{300}{x} \times \frac{20}{30} = \frac{20x}{20} \frac{9000}{20} x = 450miles[/tex]

1. The Hamiltons are installing a new pool in their backyard. The scale drawing below represents the new pool, where 1 centimeter represents 5 feet. 4 cm 6 cm If the area of the Hamiltons' backyard is 900 square feet, how many square feet of their backyard will NOT be taken up by the pool? Round your answer to the nearest whole number.​

Answers

Answer:

175

Step-by-step explanation:

Because why would i lie?

The number of square feet of their backyard will NOT be taken up by the pool should be 100 square feet.

Calculation of the number of square feet;

Since 1  centimeter represents 5 feet. 4 cm 6 cm And, the area of the Hamiltons' backyard is 900 square feet.

So here it can be like

4cm (5) = 20ft

6cm (5) = 40ft

Now

20ft : 40ft pool

20(40) = 800 square ft

So,

= 900sq ft - 800sq ft

= 100 square feet

Learn more about area here: https://brainly.com/question/17758676



5 Bill's trail mix has 6 cups of walnuts
and 10 cups of cranberries. Using
the same recipe, how many cups
of walnuts go with 15 cups of
cranberries?

Answers

Answer:

Umm, I will do my best to comment on this. I feel so bad for all the people that I hit answer and I don´t know it. =( !

Answer:

25.5

Step-by-step explanation:

10÷6=1.7

1.7x15=25.5

Solve each equation 24 = 5k - 8k

Answers

Answer:

k = -8

Step-by-step explanation:

24 = 5k - 8k

24 = -3k

k = 24/(-3)

k = -8

Answer:

k = -8

Step-by-step explanation:

Solve for k

First we re arrange our equation so that it look simple to calculate.

24=5k-8k

5k-8k = 24

-3k = 24

Divide -3 both side to get the value of k

 k = -8

To prove substitute k into formula:

5k-8k = 24

5 (-8) - 8 (-8) = 24

-40 + 64 = 24

24 = 24

The area of an ellipse with axes of length
2a and 2b is ab.
The percent change in the area when a increases by
2.74% and b increases by 2.65% is

Answers

Answer:

The area increases by 5.46261%

Step-by-step explanation:

Well firstly, the area of an ellipse is not ab, but it's proportional to ab ([tex]\pi ab[/tex] where a and b are the semi-minor and semi-major axes).

This tells us that when a increases by 2.74% and b increases by 2.65% the new area will be:

[tex]A = \pi \cdot (a \cdot 102.74\%)(b \cdot 102.65\%) = \pi a b \cdot 102.74\% \cdot 102.65\% = \pi ab \cdot 105.46261\%[/tex]

The percentage change in area of the ellipse is 5.5%

The area of an ellipse with an axes of length  of 2a and 2b is πab.

Area of ellipse = πab

Since a increases by  2.74%, hence a = (100% + 2.74%)a = 1.0274a

Also, b increases by  2.65%, hence b = (100% + 2.65%)b = 1.0265b

Therefore the new area = π * 1.0274a * 1.0265b = 1.055πab

The ratio in the area = 1.055πab/ πab = 1.055

The percentage change in area of the ellipse is 5.5%

Find out more at: https://brainly.com/question/8777183

A figure is shown.
8x
7x
44.4°
What is the measure, in degrees, of the highlighted angle?

Answers

We know that the sum of a straight line is 180° . So here there are 3 angles in a straight line . And the sum is 180° . So that ,

[tex]\tt\to Sum_{(angles \ of \ a \ straight \ line)}= 180^o \\\\\tt \to 7x + 8x + 44.4^o = 180^o \\\\\tt\to 15x = 180^o - 44.4^o \\\\\tt\to 15x = 135.6^o \\\\\tt\to x =\dfrac{135.6^o}{15}\\\\\tt\to \boxed{\orange{\tt x = 9.04^{\circ} \approx 9^{\circ} }}[/tex]

So the measure of angle that is highlighted will be 8x = 8(9) = 72°

Answer:

72.32degrees

x is 9.04

Step-by-step explanation:

7×9.04=63.28

8×9.04=72.32

44.4+63.28+72.32=180

Mr. Wilcox would really like his laptimes to be consistently between 1.75 and 1.85 minutes.
What proportion of his laps were in this range?

Answers

Answer:

Use normalcdf ( 1.75, 1.85, 1.84, 0.07 )

Doc and Marty should have laptimes between 1.75 and 1.85 approximately 45.75% of the time.

Step-by-step explanation:

Consider the following time series data. Week 1 2 3 4 5 6 Value 18 12 15 10 18 14 Using the naive method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy. (a) mean absolute error MAE = (b) mean squared error MSE = (c) mean absolute percentage error (Round your answer to two decimal places.) MAPE = % (d) What is the forecast for week 7?

Answers

Answer:

(a) MAE = 5.20

(b) MSE = 10

(c) MAPE = 38.60%

(d) Forecast for week 7 = 14

Step-by-step explanation:

Note: See the attached excel for the calculations of the Error, Error^2, and Error %.

(a) mean absolute error

MAE = Total of absolute value of error / Number of observations considered = |Error| / 5 = 26 / 5 = 5.20

(b) mean squared error

MSE = Total of Error^2 / Number of observations considered = Error^2 / 5 = 150 / 5 = 10

(c) mean absolute percentage error (Round your answer to two decimal places.)

MAPE = Total of Error % / Number of observations considered = Error % / 5 = 193.02 / 5 = 38.60%

(d) What is the forecast for week 7?

Since the forecast is based on the naive method (most recent value), the forecast for week 7 is value for week 6. Therefore, we have:

Forecast for week 7 = 14

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