State the null hypothesis H 0 and the alternative hypothesis H a in each case. B

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 74. This year 29 students who took second-year calculus passed the placement test. Choose the correct answer.

a. H0: > 74;   Ha: = 74

b. H0: = 29;   Ha: 29

c. H0: = 29;   Ha: > 29

d. H0: < 74;   Ha: = 74

e. H0: = 74;   Ha: 74

(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 slower. She measures how long each of 12 mice takes with the rap music as a stimulus. Choose the correct answer.

a. H0: = 19 sec;   Ha: > 19 sec

b. H0: = 12 sec;   Ha: < 12 sec

c. H0: = 19 sec;   Ha: 19 sec

d. H0: = 19 sec;   Ha: < 19 sec

e. H0: > 12 sec;   Ha: = 12 sec

(c) The average square footage of one-bedroom apartments in a new student-housing development is advertised to be 930 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. Choose the correct answer.

a. H0: = 930 ft2;   Ha: 930 ft2

b. H0: = 930 ft2;   Ha: > 930 ft2

c. H0: > 930 ft2;   Ha: = 930 ft2

d. H0: = 930 ft2;   Ha: < 930 ft2

e. H0: < 930 ft2;   Ha: = 930 ft2

Explanation / Answer

(a)

e. H0: = 74;   Ha: 74

Because, Scores in second-year calculus are scaled so the average each year is equivalent to a 74.

(b) a. H0: = 19 sec;   Ha: > 19 sec

Because, measures how long each of 12 mice takes with the rap music as a stimulus.

(c) d. H0: = 930 ft2;   Ha: < 930 ft2

Because,  student group thinks that the apartments are smaller than advertised. They hire an engineer to measure a sample of apartments to test their suspicion.

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