Question

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

Answer 1

Answer: (A)

`H_0:\mu=75\\H_a:\mu\\eq75`

(B)

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

(C)

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

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\\eq75`

(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<850 \ ft^2`