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4vir4ik [10]
3 years ago
14

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
Mathematics
1 answer:
padilas [110]3 years ago
7 0

Answer: (A)

H_0:\mu=75\\H_a:\mu\neq75

(B)

H_0:\mu=24\ sec\\H_a:\mu>24\ sec

(C)

H_0:\mu=850\ ft^2\\H_a:\mu

Step-by-step explanation:

  • Null hypothesis (H_0): It is a statement showing population parameters as per the objective of the study. It generally takes "≤,≥,=" signs.  
  • Alternative hypothesis (H_a): 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.

H_0:\mu=75\\H_a:\mu\neq75

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

H_0:\mu=24\ sec\\H_a:\mu>24\ sec

(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.

H_0:\mu=850\ ft^2\\H_a:\mu

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So option A will be the answer

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2 years ago
8. How many ways can a committee of 5 students be chosen from a student council of 30 students? Is the order in which the member
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Answer: A committee of 5 students can be chosen from a student council of 30 students in 142506 ways.

No , the order in which the members of the committee are chosen is not  important.

Step-by-step explanation:

Given : The total number of students in the council = 30

The number of students needed to be chosen = 5

The order in which the members of the committee are chosen does not matter.

So we Combinations (If order matters then we use permutations.)

The number of combinations of to select r things of n things = ^nC_r=\dfrac{n!}{r!(n-r)!}

So the number of ways a committee of 5 students can be chosen from a student council of 30 students=^{30}C_5=\dfrac{30!}{5!(30-5)!}

=\dfrac{30\times29\times28\times27\times26\times25!}{(120)\times25!}=142506

Therefore , a committee of 5 students can be chosen from a student council of 30 students in 142506 ways.

4 0
2 years ago
Solve the equation <img src="https://tex.z-dn.net/?f=%2835%20x%5E%7B4%7D%20y%2B14%20x%5E%7B5%7D%20y-2%20y%5E%7B3%7D-4x%20y%5E%7B
jeka94
\underbrace{35x^4y+14x^5y-2y^3-4xy^3}_M\,\mathrm dx+\underbrace{7x^5-6xy^2}_N\,\mathrm dy=0

M_y=35x^4+14x^5-6y^2-12xy^2
N_x=35x^4-6y^2

\dfrac{N_x-M_y}N=\dfrac{-14x^5+12xy^2}{7x^5-6xy^2}=-2

This suggests an integrating factor depending on x only is possible, and given by

\mu(x)=\exp\left(-\displaystyle\int\frac{N_x-M_y}N\,\mathrm dx\right)=e^{2x}

Distributing across the ODE, we end up with

\underbrace{(35x^4y+14x^5y-2y^3-4xy^3)e^{2x}}_{M^*}\,\mathrm dx+\underbrace{(7x^5-6xy^2)e^{2x}}_{N^*}\,\mathrm dy=0

The equation is now exact, with

{M^*}_y={N^*}_x=(35x^4+14x^5-6y^2-12xy^2)e^{2x}

Now we find the solution:

F_x=M^*
F=\displaystyle\int(35x^4+14x^5-2y^3-4xy^3)e^{2x}\,\mathrm dx
F=(7x^5y-2xy^3)e^{2x}+f(y)

F_y=N^*
(7x^5-6xy^2)e^{2x}+f'(y)=(7x^5-6xy^2)e^{2x}
f'(y)=0
\implies f(y)=C

The general solution is then

F(x,y)=(7x^5y-2xy^3)e^{2x}=C
7 0
3 years ago
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