A.5 Answer: TW 5 tutorial

Answers for Sect. 5.2

1. A few issues: Five decimal places is to the nearest $$0.01$$ of a mm! The standard deviation of the difference is not the difference between the individual standard deviations. A standard deviation cannot be negative. (Same applies to standard errors, but we aren't there yet.) Note that there is a sample size of $$0$$ for the difference!
2. A few issues: Five decimal places: That's accuracy to $$0.00001$$ of a millimetre per second (I don't think so...). There is no numerical measures of the most important thing and the thing the RQ (presumably) concerns: The differences between the two brands.

Answers for Sect. 5.3

1. A few issues: vertical axis is not labelled (presumably burn time in seconds); horizontal axis is not labelled (we have no way of knowing what is happening there.)

2. A few issues: this is not a summary: this shows the burn-time of every individual candle, and makes it hard to compare means (which is the RQ); why is every bar labelled, which just adds unnecessary clutter; fonts are hard too read (small); a boxplot (or dotchart) would be the appropriate graph. In addition: the largest value is over $$70$$ mins! Do a quick project!

3. A few issues: Compares just two numbers (means) using lots of ink; no indication of variation in the data; a boxplot (or dotchart) would be appropriate.

Answers for Sect. 5.4

1. Plot 1: $$0.94$$ (correlation D); Plot 2: $$-0.95$$ (correlation A); Plot 3: $$0.12$$ (correlation B); Plot 6: $$0.75$$ (correlation C).
Correlation is inappropriate for Plot 4 (non-linear) and Plot 5 (non-linear).
2. Examples of the direction in Plot 1: any two variables moderately positively correlated, such as height and weight, distance lived from university and travel time, etc.
3. Examples of direction in Plot 2: any two variables moderately negatively correlated, such as hours of weekly exercise and body weight, number of SCI110 tutorial missed and final mark, etc.
4. Plot 1: $$88.4$$%; Plot 2: $$90.3$$%; Plot 3: $$1.4$$%; Plot 6: $$56.3$$%.

Answers for Sect. 5.6

Answers implied by H5P.

1. Five variables. ('Participants' would not be summarised, it is technically an identifier and not a variable, as each person has a unique value).
2. Age; Height; Weight and quantitaive continuous.
3. Gender (nominal; two levels); GMFCS (ordinal; three levels)
4. As follows:
• 'Gender': Percentages (or number) F and M
• 'Age': Mean/median; standard deviation/IQR
• 'Height': Mean/median; standard deviation/IQR
• 'Weight': Mean/median; standard deviation/IQR
• 'GMFCS': Percentages (or numbers) in each group
5. As follows:
• 'Gender': Barchart (not really needed)
• 'Age': Histogram/stemplot
• 'Height': Histogram/stemplot
• 'Weight': Histogram/stemplot
• 'GMFCS': Barchart/piechart
6. As follows:
• Between Gender and Height: Boxplot
• Between Gender and GMFCS: Side-by-side or stacked bar chart.

Answers for Sect. 5.7.1

1. Relational.
2. Observational: no intervention
3. O: average accuracy. Response variable: the 'accuracy' for each individual.
4. C: Between blind and sighted individuals. Explanatory variable: Whether the individual is blind, or not.
5. No intervention: the C (whether someone is blind or not) cannot be manipulated by the researchers.
6. Quantitative continuous.
7. Qualitative nominal.
8. A boxplot.
9. The unit of analysis is the person.
10. $$34 + 36 = 70$$.
11. One: each person gets one 'accuracy' value.

Answers for Sect. 5.7.2

1. Not shown.
2. The median temperatures similar; a slight increase from Office A to C. IQR similar for each office, and range similar for Offices A and C (slightly larger for Office B). In summary: Office A a bit different (cooler) on average.
3. Perhaps Office A.

Answers for Sect. 5.7.3

1. Stacked or side-by-side barcharts; whether bird injured or not, and whether upper or lower are both qualitative variables.
2. Boxplots would be OK; one quantitative (length-of-stay) and one qualitative (therapy type) variable.
3. Scatterplots; two quantitative variables (frequency; amount wheat consumed).
4. Two-way table or stacked/side-by-side barchart, or table; two qualitative variables vars ($$30$$ mins of physical activity or not; vigorous physical

Answers for Sect. 5.7.4

Answers implied by H5P.

1. Explanatory variable is the number of hours of light each plant received; response variable is the number of flowers each plant received. The units of observation are the individual plants.
2. Explanatory variable is the number of smokers at the restaurant; response variable is the concentration of fine particulate matter.
3. Response variable is the waiting time; explanatory variable is the time of admission.
4. Explanatory variable is the "Level of Playfulness"; response variable is the "Level of Coping".

Answer for Sect. 5.7.5

1. To display the relationship between the age of athletes, and the times taken for each athlete to complete the `beep test': Scatterplot
2. To display the percentage of elderly people in nursing homes that can independently complete a given task, for each of the seven tasks on a given list: Bar chart or Dot chart
3. To display the relationship between the type of fertiliser applied to a vegetable crop (either A, B or C) and the yield per hectare, measured over numerous plots: Boxplot
4. To display the distribution of the hardness measurements taken of 250 samples of bamboo: Histogram
5. To display the relationship between the age of concrete test cylinders (under $$5$$ years; $$5$$ years and older) and their strength (fit for purpose; or not fit for purpose): Side-by-side or stacked bar chart

Answers for Sect. 5.7.6

1. Observational; the ant nest would be pre-existing.
2. Both are 'ant nests'.
3. Looks good!
4. Uphill looks different to the other two. Also: the lower dots comprise mostly blue dots (Sourdough Trail), so perhaps a difference between locations too.

Answers for Sect. 5.7.7

1. True experiment: treatments given (experiment), and the researchers selected the groups, groups did not previously existed (so true experiment).
2. Observation: each patient. Analysis: The patient.
3. Pretty good. A label on the horizontal axis would be better, but the caption does contain that information.
4. Pain is reduced.
5. Yes, probably. We cannot be sure due to randomness...

Answer for Sect. 5.7.8

Boxplot; scatterplot.