University:
Washington State University
Course:
MATH 172 | Calculus II
Academic year:

2024
Views:

289

Pages:

4
Author:

Bailey Ayala

Question 1 Hypothesis Testing Using the P-value Approach: Answer: Null Hypothesis ( 𝐻 0 H 0 ): 𝑝 = 0.52 p=0.52 Alternative Hypothesis ( 𝐻 1 H 1 ): 𝑝 < 0.52 p<0.52 𝑁 = 150 N=150, 𝑋 = 72 X=72, 𝛼 = 0.1 α=0.1 Check requirements: 𝑁 𝑝 ( 1 − 𝑝 0 ) = 150 ⋅ 0.48 ⋅ 0.52 = 37.44 > 10 Np(1−p 0 )=150⋅0.48⋅0.52=37.44>10 Requirements are satisfied. Compute the sample proportion: 𝑝 = 𝑋 𝑁 = 72 150 = 0.48 p= N X = 150 72 =0.48 Compute the test statistic ( 𝑧 z): 𝑧 = 𝑝 − 𝑝 0 𝑝 0 ( 1 − 𝑝 0 ) 𝑁 = 0.48 − 0.52 0.52 ⋅ 0.48 150 = − 0.98 z= N p 0 (1−p 0 ) p−p 0 = 150 0.52⋅0.48 0.48−0.52 =−0.98 Find the P-value: Using Excel or a normal distribution table: 𝑃 ( 𝑍 < − 0.98 ) = 0.1635 P(Z<−0.98)=0.1635 Conclusion: Since 𝑃 = 0.1635 > 𝛼 = 0.1 P=0.1635>α=0.1, fail to reject 𝐻 0 H 0 . There is not enough evidence to conclude 𝑝 < 0.52 p<0.52. Question 2 Examples of Sampling Distributions: Answer: Mean trout lengths based on samples of size 5. Average male height based on samples of size 30. Question 3 Generating 12 Random Numbers Between 01 and 99: Answer: Using the provided numbers: 78 , 03 , 80 , 22 , 84 , 75 , 52 , 31 , 46 , 12 , 70 , 91 78,03,80,22,84,75,52,31,46,12,70,91 Steps: Pair digits sequentially to form numbers: 78 , 03 , 80 , … 78,03,80,…. Exclude any numbers outside 01–99. Question 4 Simulating Basketball Performances: Answer: (a) Basketball player makes 40% of 25 shots: Let numbers 1 − 40 1−40 represent made shots, and 41 − 100 41−100 represent missed shots. Use the random number generator randint(1,100,25) randint(1,100,25). Count numbers 1 − 40 1−40 to estimate made shots. (b) Basketball player makes 75.2% of 8 free throws: Let numbers 1 − 752 1−752 represent made free throws, and 753 − 1000 753−1000 represent missed throws. Use randint(1,1000,8) randint(1,1000,8). Count numbers 1 − 752 1−752 for made throws. Question 5 Relative vs. Frequency Distributions: Answer: Relative frequency distributions: Show proportions or percentages, allowing comparisons across datasets of different sizes. Useful when large datasets might overshadow smaller ones if only raw frequencies are used.