**6.55 More on determining hypotheses.** State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_a \) 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 77. This year, 21 students who took second-year calculus passed the placement test. **Transcription for Educational Website:****b) Experiment on Learning in Animals:**Researchers often conduct experiments on learning in animals by measuring the time it takes for a mouse to navigate a maze. In this particular study, the mean time recorded for completing the maze is 20 seconds. The researcher posits that exposure to rap music might slow down the mice's navigation. To test this hypothesis, the researcher measures the time it takes for each of 12 mice to traverse the maze while listening to rap music as a stimulus.**c) Evaluating Apartment Advertisements:**In a new student-housing development, the advertised average size for one-bedroom apartments is 880 square feet. However, a group of students suspects that the actual apartment sizes are smaller than stated. To investigate their suspicion, they employ an engineer to measure the square footage of a sample of the apartments.

The question is about hypo. testing Introduction : 1 ) If claim / research statement has =, ≥ or ≤ sign, then it goes under null hypo. 2 ) If claim / research statement has ≠, < or > sign, then it goes under alt. hypo. To find : State null and alt. hypo. for each given 3 sub-parts also identify parameters used in hypo. a ) Given : Avg. scores in 2nd year calculus ( μ ) = 77 Research statement : Student who get credit differs in their success with 2nd year calculus The word " differ " indicates the " ≠ " sign. Hence, this statement goes under alt. hypo. Null and alt. hypo : H0 : μ = 77Ha : μ ≠ 77 The parameter used in this hypo. is popl. mean / avg. ( μ ) b ) Given : The mean time taken to complete one particular maze ( μ ) = 20 seconds Research statement : The rap music will cause the mice to complete the maze more slowly The sentence " to complete the maze more slowly " indicates the " > " sign that means it requires more time to complete the maze Hence, this statement goes under alt. hypo. Null and alt. hypo. : H0 : μ = 20Ha : μ > 20 The parameter used in this hypo. is popl. mean ( μ ) c ) Given : The avg. sqft. of 1 bedroom apartments is advertised ( μ ) = 880 sqft. Research statement : A group of students thinks that the apartments are smaller than advertised The word " smaller " indicates the " < " sign Hence, this statement goes under alt. hypo. Null and alt. hypo. : H0 : μ = 880Ha : μ < 880 The parameter used in this hypo. is popl. avg. ( μ )