1.1 A – Identify population & sample (Pew Research)
Context: 1500 U.S. adults were asked: “do you think there is solid evidence for global warming?” 855 said yes.
(a) Identify the population. (b) Identify the sample. (c) Is the value “855” a parameter or statistic? Explain.
→ Population: The collection of all U.S. adults (their responses regarding global warming). [ref: p.8-9]→ Sample: The 1500 U.S. adults who actually responded. [ref: p.9]→ 855 yes’s: This is a statistic because it describes the sample (855/1500 = 57%). If it were the proportion of all U.S. adults, it would be a parameter. [ref: p.10-11]
1.1 B – Parameter or statistic? (petroleum engineers / Northwestern)
1) A survey of a sample of college career centers reported average starting salary for petroleum engineering majors = $83,121.
2) The 2182 students who accepted admission to Northwestern in 2009 have an average SAT score of 1442.
#1 salary $83,121: based on a sample → sample statistic. [p.11]#2 SAT 1442: based on all 2009 admitted students → describes the population (that specific cohort) → population parameter. [p.12]💡 Even if the population is “all 2009 admits,” it’s still a parameter because it uses every individual of interest.
1.1 C – descriptive & inferential (longevity study)
A sample of men aged 48 was followed 18 years: 70% unmarried men alive at 65, 90% married men alive at 65. (Source: Journal of Family Issues)
a) Which part is descriptive? b) Give a possible inference.
Descriptive: the reported percentages “70% of unmarried in sample alive at 65” and “90% of married” — they summarize the observed data. [p.15]Inferential: “Being married is associated with longer life for men” (a conclusion that extends beyond the sample to the population). Also possible: “marriage may have a protective effect.” [p.15]
1.1 D – classify each value
(i) In a survey of 500 students, 62% prefer online learning. (ii) The registrar reports that exactly 12,840 students are enrolled at your university (all records).
(i) 62% based on 500 → statistic (sample).(ii) 12,840 is from entire enrollment → parameter (population).
1) Effect of changing flight patterns on accident numbers. 2) Effect of oatmeal on lowering blood pressure. 3) How 4th graders solve a puzzle. 4) U.S. residents’ approval of the president.
1) Flight/accidents:Simulation (impractical/dangerous to create real changes). [p.31]2) Oatmeal & BP:Experiment – apply treatment (eating oatmeal) vs control. [p.32]3) Puzzle solving:Observational study – watch & measure without intervention. [p.33]4) Approval rating:Survey – ask individuals. [p.34]
1.3 B – sampling: majors vs random numbers
You study opinion about stem cell research on campus.
(A) Divide by major, randomly pick some from each major.
(B) Assign each student a number, generate random numbers, question those selected.
(A) groups = majors → random from each group → stratified sampling. [p.42](B) every student equally likely, random numbers → simple random sample. [p.43]
1.3 C – more sampling names
i) Choose every 50th household from a list. ii) Divide city into city blocks, randomly pick 5 blocks and survey all households in those blocks. iii) Stand outside library and ask people.
i) every kth → systematic. [p.41]ii) blocks = clusters, all members in selected clusters → cluster sample. [p.40]iii) library intercept → convenience (non‑probability).
1.3 D – classify study design
a) A medical researcher gives a new drug to some patients and a placebo to others, then measures cholesterol. b) A sociologist examines public records to determine the correlation between crime rate and unemployment.
a) treatment assigned → experiment.b) no manipulation, just observes existing data → observational study.
1.3 E – Stratified or cluster?
A school has 4 grades (9‑12). To estimate average screen time, you randomly select 15 students from each grade.
Grades are natural strata (homogeneous within? maybe). You sample from every stratum → stratified.If you instead selected two entire grades (all students) it would be cluster.
1.3 F – identify from study
A researcher wants to know the average height of women aged 30 in Ohio. She measures 250 women and finds a mean of 164 cm. Is 164 cm a parameter or statistic?
164 cm describes the sample of 250 women, so it’s a statistic. If she measured every woman in Ohio aged 30, it would be a parameter.
1.3 G – design a experiment (control group)
You want to test whether a new teaching method improves exam scores. Describe a basic experimental design.
Take a random sample of students, randomly assign them to two groups: treatment (new method) and control (traditional). Compare final exam means. Control for teacher effect, time of day, etc. Ideally double‑blind.
1.3 H – simulation scenario
Why would a car manufacturer use crash test dummies and computer models instead of real humans?
Ethical and practical reasons: simulation reproduces conditions without risk. Also cheaper and repeatable.
1.3 I – identify possible errors
In a telephone survey about internet usage, only landline numbers are called. What bias might occur?
Undercoverage: households with only cell phones (often younger, lower income) are excluded. So sample not representative → nonresponse/coverage bias.
1.3 J – simple random sample procedure
731 stats students, you need a sample of 8. Using random digits, you start at row 3 col 2: 719, 662, 650, 004, 053, 589, 403, 129. Explain why 004 is included and why numbers > 731 are ignored.
Assign numbers 001–731. Read three‑digit groups. Ignore 000 and 732–999 because they don’t correspond to any student. 004 represents student #4. This gives each student an equal chance (simple random sample). [p.38]
⚡ extra 1.1–1.3 recap ⚡
Mixed – classify each statement
1) “52% of the sampled likely voters approve.” → parameter/statistic? 2) “The median household income in the US (from census) is $70,784.” → parameter/statistic? 3) Descriptive or inferential: “The correlation in the sample was -0.4, suggesting a negative relationship in the population.”
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