Need some questions answered from INTRO TO STATS
DO NOT TAKE ON THIS ASSIGNMENT IF YOU DON’T KNOW WHAT YOU ARE DOING!
Need 1-19 multiple choice answered and then 2 case studies answered.
FYI: You will need a z-table and t-table to complete this exam.
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?
𝐻”:
𝐻$:
3.) [4 pts] Describe what a Type I and Type II error would entail in this scenario, and what the consequences of making
each one would be.
Type I Error:
Type II Error:
4.) [5 pts] Using your mean and standard deviation you calculated in part (1.), construct a 95% confidence Interval for
the true mean pH level of Lake 153.
5.) [2 pts] Interpret your confidence interval you just calculated in part (4.).
6.) [5 pts] Test the hypothesis from part (2.) at the 𝛼 = 0.05 level using the critical value approach.
7.) [3 pts] What is the approximate p-value of your test in part (6.)?
8.) [5 pts] Based on your above results in parts (4.), (6.), and (7.), should the Department of Fish and Wildlife be
concerned about the acidity of Lake 153? Be sure to justify your decision using the results from above.
Case Study 2: In the United States, 69.8% of high school graduates enrolled in college in the fall immediately following
their high school completion in 2016 (the most recent year full data is available, according to the National Center for
Education Statistics). Pasco School District designed a study to see how their own high school graduates compare to
nationwide trends.
The Sampling: To perform this study, analysts randomly selected and contacted 500 adults who had received their high
school degree from a school in the Pasco School District during the years of 2010-2018. After conducting the survey, it
was found that 388 of the 500 surveyed had attended college in the fall immediately following their high school
completion.
9.) [5 pts] Calculate the sample proportion (𝑝) of Pasco High School graduates who immediately attended college after
receiving their diploma.
10.) [2 pts] For the school district, they initially hypothesized (and hoped to be able to show) that the percentage of
Pasco School District graduates that went on to immediately attend college was higher than the 2016 national rate.
Formulate the formal hypothesis statement that best describes this study.
𝐻”:
𝐻$:
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?
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Math 146
Final Exam Practice Test
Your final exam will be a combination of multiple choice problems and two case studies (one for means, one for proportions) that will put together most of the concepts you have learned up to this point. The following is an example of a case study similar to the one you will be presented.
The Scenario: The production line manager at a factory which produces PVC-Pipe fittings needs to run a quality check on the machine producing elbow fittings for ½” PVC piping. The elbow fittings are supposed to be produced with an average mass of 60g. If the machine is producing lighter fittings it could compromise the integrity of the product, but if the machine is producing heavier fittings there is likely waste occurring.
The Sampling: To test if the machine is calibrated correctly, the manager randomly selects 12 PVC fittings off the production line, with the following results:
Sample
1
2
3
4
5
6
7
8
9
10
11
12
Mass (g)
60.1
60.7
60.6
60.5
59.9
60.4
59.9
60.2
60.7
59.8
60.3
60.4
1.) Calculate the mean and standard deviation of the mass of the PVC elbows.
2.) As the manager, what would be the appropriate hypothesis test to perform in this scenario? (State the formal hypothesis test using )
3.) Describe what a Type I and Type II error would entail in this scenario, and what the consequences of making each one would be.
4.) Based on your answer in part (3.), which type of error (Type I/Type II) would you rather commit? Based on this, would you test this hypothesis at the, or the level?
5.) Based on the -level you chose in part (4.), calculate a Confidence Interval for the true mean mass of the elbows being produced.
6.) Test the hypothesis from part (2.) at the -level you chose in part (4.).
7.) What is the approximate p-value of your test in part (6.)?
8.) Based on your above results in parts (5.), (6.), and (7.), should the manager be concerned about the calibration of the machine? Be sure to justify your decision using the results from above.