Need some questions answered from INTRO TO STATS

Final Exam Math 146 Name: ___________________________________________________ Case Studies: (30 Points Each, Values Individually Marked) Two case studies are presented, and for each you will use concepts we have learned throughout the quarter to perform an analysis of the data and come to some conclusions. Case Study 1: Researchers with the Department of Fish and Wildlife (DFW) monitor the acidity of lakes in the Cascade Mountains. Pollution in the atmosphere can mix with water and oxygen and create “acid rain”. When this falls at high altitudes, the runoff can cause acidity in lakes to rise. A rise in acidity can be harmful to the ecosystems of the lakes at high altitudes. Acidity is measured on the pH scale, with 7 being neutral, lower pH being more acidic, and higher pH being less acidic (basic). The DFW begins to be concerned about the acidity of freshwater lakes when the pH drops below 6. The Sampling: Each year, the DFW randomly selects a few new lakes to monitor. Then, over the course of three years, the DFW visits each lake four times/year and takes a random sample of water to test for acidity. For one particular lake, Lake 153, the past three years of samples produced the following pH levels: Sample W16 Sp16 Su16 F16 W17 Sp17 Su17 F17 W18 Sp18 Su18 F18

pH 6.2 6.4 5.9 5.5 5.9 6.1 6.0 5.8 5.5 5.8 5.4 5.8

1.) [4 pts] Calculate the mean and standard deviation of the pH levels of Lake 153. 2.) [2 pts] As a data analyst for the DFW, you are concerned in pH levels dip below 6.0. How would you formulate this as

a formal hypothesis test?

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3.) [4 pts] Describe what a Type I and Type II error would entail in this scenario, and what the consequences of making each one would be.

Type I Error:

Type II Error:

4.) [5 pts] Using your mean and standard deviation you calculated in part (1.), construct a 95% confidence Interval for the true mean pH level of Lake 153.

5.) [2 pts] Interpret your confidence interval you just calculated in part (4.). 6.) [5 pts] Test the hypothesis from part (2.) at the 𝛼 = 0.05 level using the critical value approach. 7.) [3 pts] What is the approximate p-value of your test in part (6.)? 8.) [5 pts] Based on your above results in parts (4.), (6.), and (7.), should the Department of Fish and Wildlife be

concerned about the acidity of Lake 153? Be sure to justify your decision using the results from above.

Case Study 2: In the United States, 69.8% of high school graduates enrolled in college in the fall immediately following their high school completion in 2016 (the most recent year full data is available, according to the National Center for Education Statistics). Pasco School District designed a study to see how their own high school graduates compare to nationwide trends. The Sampling: To perform this study, analysts randomly selected and contacted 500 adults who had received their high school degree from a school in the Pasco School District during the years of 2010-2018. After conducting the survey, it was found that 388 of the 500 surveyed had attended college in the fall immediately following their high school completion. 9.) [5 pts] Calculate the sample proportion (𝑝) of Pasco High School graduates who immediately attended college after

receiving their diploma. 10.) [2 pts] For the school district, they initially hypothesized (and hoped to be able to show) that the percentage of

Pasco School District graduates that went on to immediately attend college was higher than the 2016 national rate. Formulate the formal hypothesis statement that best describes this study.

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𝐻$: 11.) [2 pts] Describe what a Type I and Type II error would entail in this scenario, and what the consequences of making

each one would be.

Type I Error:

Type II Error:

12.) [5 pts] Use your sample proportion from part (9.) to construct a 99% confidence interval for the true proportion of Pasco School District students that immediately attended college upon completion of their diploma.

13.) [2 pts] Interpret your interval from part (12.). 14.) [8 pts] Test your hypothesis from part (10.) at the 𝛼 = 0.01 level using the critical value approach. 15.) [3 pts]Calculate the p-value of your test in part (14.). 16.) [3 pts] Based on your results in parts (12.) and (14.), and (15.) is there evidence that Pasco School District students

have a higher rate of immediately attending college than the nationwide rate?