Question

State the null hypothesis H 0 and alternative hypothesis H a Ha in each of the following cases.

(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 79. This year 21 students who took second-year calculus passed the placement test.

H 0 :μ=79 H0:μ=79 versus H a :μ<79

H 0 :μ=79 H0:μ=79 versus H a :μ>79

H0:μ=79 versus H a :μ≠79

(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 19 seconds for one particular maze. A researcher thinks that playing rap music will cause the mice to complete the maze more slowly. She measures how long each of 12 mice takes with the rap music as a stimulus.

H 0 :μ=19 H0:μ=19 versus H a :μ≠19

H 0 :μ=19 H0:μ=19 versus H a :μ>19

H 0 :μ=19 H0:μ=19 versus H a :μ<19

(c) The average square footage of one-bedroom apartments in a new student-housing development is advertised to be 860 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.

H 0 :μ=860 H0:μ=860 versus H a :μ≠860

H 0 :μ=860 H0:μ=860 versus H a :μ>860

H 0 :μ=860 H0:μ=860 versus H a :μ<860

and explain the reasons each.

Answer 1

(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 79. This year 21 students who took second-year calculus passed the placement test.

C) H0:μ=79 versus H a :μ≠79 ## will be Correct null and Alternative Hypothesis

Alternative hypothesis is clearly explain ie

The mathematics department wants to know if students who get credit in this way differ in their success with second-year calculus.

differ means Exact not Equal to 79

(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 19 seconds for one particular maze. A researcher thinks that playing rap music will cause the mice to complete the maze more slowly. She measures how long each of 12 mice takes with the rap music as a stimulus.

C) H 0 :μ=19 H0:μ=19 versus H a :μ<19 $$ will be Correct null and Alternative Hypothesis

Explain: A researcher think that playing rap music will cause the mice to complete the maze more slowly.

that mean they claim that time will be time will be needed more for playing rap music

hence this is running more slow ie less than expexted < 19 seconds

(c) The average square footage of one-bedroom apartments in a new student-housing development is advertised to be 860 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.

H 0 :μ=860 H0:μ=860 versus H a :μ<860 %%$$ will be Correct null and Alternative Hypothesis

Explain: we are clearly see that students are claim that apartment are smaller than advertised ie less than 860Square feet.