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# Confidence Interval computation raw responses

Anonymized and given a public identifier, these are the raw student responses from the administration of the integrated assessment instrument scored against the Quantitative Scientific Reasoning general education goal of the Community College of Allegheny County (serving the greater Pittsburgh area).

## codeDAT-102: Introduction to data analytics

#### Student response ticketID: 126.263

Interpretation:
1
Representation:
2
Calculation:
4
Application/analysis:
1

#### Student response ticketID: 126.148

Interpretation:
2
Attempt made at interpretation but content is erroneous; stability is a possible notion to invoke, but it is not explained. Fragmentary writing fails to convey accurate statistical notions.
Representation:
2
UofA is a neighborhood resident, not the respondent's "hours"; population is correct;
Calculation:
2
Sample size of 30 is incorrect as 15 were sampled from each sub-population. The respondent's point estimate of 1.385 is not found on poster for 126.263: Opinions of 5G tower and no computations are shown for the Standard error. Unfortunately, project 126.263 does not clearly lay out what the mean is actually an average of--we assume the average of Question 2 buy neighborhood. Due to this confusion, this value is not verifiable without additional input on student process.
Application/analysis:
2
No concrete connection of resident opinions and statistical concept

#### Student response ticketID: 126.149

Interpretation:
1
No response
Representation:
2
Seemed to copy a phrase from the 126.150: HR Contact poster "Regular employees at [company x]" since population sampled as "entire population" is not coherent conceptually
Calculation:
1
No response
Application/analysis:
1
No response

#### Student response ticketID: 126.150

Interpretation:
3
Response alomst makes to a 4 and nicely mentions the specificity and confidence tradeoff but does not draw out the notion of the population mean being the value in question.
Representation:
2
UofA is A car in a parking lot, not visual age of cars. Responded confused this with response variable.
Calculation:
2
Point estimate is target visual age mean, which is a valid reponse from Car Value at WalMart and Target but the CIs around that estimator were drawn from an unkown sourse. Car Value at WalMart and Target even provided the 95-percent CI in project but this did not get correctly transfered to form. Rather, student attempted to use a valid equation but inserting incorrect SE (no differentiation between sample SD and standard error of our population estimator)
Application/analysis:
2
Does not meaningfully connect to context of cars in shopping store parking lots.

#### Student response ticketID: 126.151

Interpretation:
1
Representation:
2
Calculation:
4
Application/analysis:
1

#### Student response ticketID: 126.152

Interpretation:
3
Precise intepretation which clarifies true versus population means. Nothing about repeated samples, however.
Representation:
3
UofA is a house, not "houses" but the population is a neighborhood.
Calculation:
3
Correct use of "s over root n" for computing SE. Where the response point estimate of 1.432 came from on Support of 5G Tower is unclear. Perhaps student computed the average of one of the neighborhoods? Cannot award 4 without verification. Support of 5G Tower tabular output on poster did not clearly connect which question the summary data relates to.
Application/analysis:
2

#### Student response ticketID: 126.153

Interpretation:
3
Correct differentiation between sample and population mean, but interpretation of the confidence as "meaning" a higher range is not tight enough to the notion of repeated sample behavior
Representation:
3
UofA is a student, not "students", but close! Population is not the SAT scores of the students at Pitt, it's the students at Pitt who use the library to study at tables.
Calculation:
4
Correct use of "s over square root of n" to generate SE and compute CIs from the mean SAT score with SD of 292.744 reported in Race and College Testing
Application/analysis:
3
Connection of domain to sample and population confidence

#### Student response ticketID: 126.154

Interpretation:
4
Connected the notion of confidence with certainty concerning population param
Representation:
2
UofA in Drinks at Dunkin is a customer, not "hot drinks bought by men", and the population sampled listed is a really a sub-population or segment of gendered customers.
Calculation:
3
Drinks at Dunkin did not actually implement the notion of a population proportion, so student response gets a 3 for ability to apply this notion that was not given much weight in class to this project with professor's guidance during class. The origins of sd=root(npq) is not clear, but related to SE = sqrt(pq) over sqrt(n)
Application/analysis:
4
Accurate application of a proportion over 0.5 to "most men"

#### Student response ticketID: 126.165

Interpretation:
1
No response
Representation:
2
126.239 is actually about hockey. UofA is a game, not "games win"; This really should be a 1.5, since 126.235 shows more fidelity to the original project, whereas this student did not even extract correctly, but attempt was made, so rating of 1 is misleading.
Calculation:
3
2Hockey First Point does not appear to have a point estimate at 13.742. Need to look into spreadsheet.
Application/analysis:
1
No response

#### Student response ticketID: 126.217

Interpretation:
1
no response
Representation:
2
Concpts of gas and week day were extracted from Price of Gas but not connected to the cocneptual markers of unit of analysis etc correctly.
Calculation:
4
Unverified from Price of Gas but numeric relationship is correct. Student selected Wed and Thu mean price for point estimate; TODO: Need to ask for notes about which point estimate.
Application/analysis:
1
No response

#### Student response ticketID: 126.235

Interpretation:
1
No response
Representation:
2
Values extracted from Price of Gas correctly but not converted correctly: Unit of analysis was not price, it is a gallon of gas.
Calculation:
3
Unclear where 2.834 came from since no mean for any day was 2.83 when only looking at Price of Gas poster. Precision of student response point estimate is higher than listed in the project. Perhaps student author was working with 126.235 with the raw data in a spreadsheet. ecd assuming incorrect value
Application/analysis:
1
No response

#### Student response ticketID: 126.236

Interpretation:
2
Notion of confidence versus precision is stated, but weakly grasped as it is padded with fluff. Respondent contrasts "confidence interval" with "bounds" which we would generally think of conceptually the same.
Representation:
2
Incorrect UofA listed as "Age value"; UofA is a car. Listing "cars in target lots" as population is confusing a sub-population for a segmented larger population.
Calculation:
2
The point estimate value of 0.776 is not found in the poster or spreadsheet on 126.152: Driving to Target and Walmart and respondent didn't norm against listed 95-percent CI on poster.
Application/analysis:
2
No explicit connection between cars and conceptual framework

#### Student response ticketID: 126.237

Interpretation:
2
Response is not conceptually coherent even when using key terms. It is true that a CI is computed from sample data, but not just sample data.
Representation:
3
U of A is a car, not "visual age of cars" as respondent indicated; Pop correctly identified
Calculation:
3
Respondent extracted the average visual age of cars in the Target lot: 0.765 and incorrectly computed confidence intervals at all levels from 126.152: Drivers to Target and Walmart. Respondent's answers should have overlapped with the 95-percent interval computed by the investigator of 126.152. Respondent transferred the formula: "statistic +- z * SE" and does list Z values next to each interval--earning this respondent a 3 instead of a 2
Application/analysis:
2
No explicit connection between cars and CI content terms

#### Student response ticketID: 126.239

Interpretation:
2
Response does not differentiate between population and sample mean.
Representation:
2
U of A is a football player, not "High School SPARQ"; ecd lacking domain knowledge here; Unclear where student's n=28 came from
Calculation:
4
The 110 comes from the NFL SPARQ (bin) vs Count of NFL SPARQ figure on Football Althetic SPARQ. Mean is pulled up from "center" by upper outliers. Student CIs shaped correctly*
Application/analysis:
2
Student does not connect to football domain

#### Student response ticketID: 126.257

Interpretation:
2
Difficult to read; not coherent conceptually.
Representation:
2
"Purchase food" is not the unit of analysis, which is a customer; population correct
Calculation:
3
No computations drawn from 126.235: Gender drinks due to the lack of a point estimate in mean form. This is an unclear rating situation since the student could not demonstrate the skill without quite a bit of computation on the raw data, but cannot be assessed on this axis. Inputting a 3 based on in person talk about why proportions would need to be computed.
Application/analysis:
1
No concrete connections between stats and customers, drinks, or gender

#### Student response ticketID: 126.258

Interpretation:
1
No response
Representation:
2
UofA is a hockey team, not "goals"; a sub population was listed instead of a population
Calculation:
2
Student response point estimate of 2.83 cannot be found in the data table on Scoring First in Hockey. Did not connect the notion of a mean with that of a point estimate
Application/analysis:
1
No response

#### Student response ticketID: 126.260

Interpretation:
2
Respondent seems to have assembled fragments of definitions of core concepts into an overall inaccurate response: the CI percentage conveys the number of instances of repeated trials one could reasonably expect to capture the "true" population mean value of the sampled random variable.
Representation:
2
UofA is a bus route, not respondent's "Pittsburgh Busses" which is more like a population. The population sampled is a subset of PA busses which are reported by the WPRDC. Respondent probably computed. Follow up. "s over root n" input values not given. TODO: ask students to show plug and play values.
Calculation:
3
Unable to find any reference to respondent's reported sample size of 1154 in written doc or spreadsheet from 126.153: PGH Bus Times. Also could not find 1904.454 anywhere, but the bounds get wider.
126.
Application/analysis:
2
No concrete connections between busses and statistics.

#### Student response ticketID: 126.263

Interpretation:
2
A strong candidate for a 2.5 if there ever was one! Respondent made solid attempt at explaining how confidence relates to a population of cars, but fundamentally misconstrues the percent value associated with a confidence interval as the fraction of the population bounded by the interval.
Representation:
3
UofA is a single car, not respondent's "Cars". Population precisely are cars which may visit Target and/or Walmart.
Calculation:
2
A strong candidate for a 2.5 if there ever was one! Extraction of the respondent's 0.744 point estimate does not appear on 126.152: Drivers to Target and Walmart poster. Nor was it found in the spreadsheet of raw data. Interval widens as expected. SE computation appears erroneous
Application/analysis:
2
Did attempt a connection to cars, but in the incorrect interpretation of confidence interval