State the null hypothesis H0 and the alternative hypothesis Ha in each case. Be

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 71. This year 20 students who took second-year calculus passed the placement test.

H0: = 20; Ha: > 20

H0: = 20; Ha: 20

H0: > 71; Ha: = 71

H0: = 71; Ha: 71

H0: < 71; Ha: = 71

(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 26 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 10 mice takes with the rap music as a stimulus.

H0: = 26 sec; Ha: > 26 sec

H0: > 10 sec; Ha: = 10 sec

H0: = 26 sec; Ha: 26 sec

H0: = 10 sec; Ha: < 10 sec

H0: = 26 sec; Ha: < 26 sec

(c) The average square footage of one-bedroom apartments in a new student-housing development is advertised to be 820 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: = 820 ft2; Ha: 820 ft2

H0: < 820 ft2; Ha: = 820 ft2

H0: = 820 ft2; Ha: < 820 ft2

H0: > 820 ft2; Ha: = 820 ft2

H0: = 820 ft2; Ha: > 820 ft2

Explanation / Answer

Answers:

(a) H0: = 71; Ha: 71 (Hint: differ in their success with second-year calculus)

(b) H0: = 26 sec; Ha: > 26 sec (Hint: maze slower)

(c) H0: = 820 ft2; Ha: < 820 ft2 (Hint: smaller than advertised)

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