VCE General Maths Data Analysis 2022 Mini Test 2

Use the following information to answer Questions 9–11.

Table 1 summarises the results of a study that compared the effectiveness of individual and group instruction (instructional method) when training future basketball referees.

Table 1

Test grade	Instructional method
	Individual	Group
A (85% or above)	10	18
B (75–84%)	35	30
C (65–74%)	30	24
D (50–64%)	28	48
E (less than 50%)	12	6
Total	115	126

In this table, test grade is the response variable and instructional method is the explanatory variable.

Question 1 [2022 Exam 1 Q9]

The variables test grade (A, B, C, D, E) and instructional method (individual, group) are

• A. a numerical and a categorical variable respectively.
• B. both nominal variables.
• C. a nominal and an ordinal variable respectively.
• D. both ordinal variables.
• E. an ordinal and a nominal variable respectively.

Question 2 [2022 Exam 1 Q10]

Of the students who received an A grade, the percentage who were instructed individually is closest to

• A. 9%
• B. 22%
• C. 36%
• D. 56%
• E. 64%

Question 3 [2022 Exam 1 Q11]

To become a qualified referee, a grade of A or B on the test is required. Those who receive a C, a D or an E will not qualify.
Using column percentages, a new two-way percentage frequency table is constructed from the data in Table 1.
In this new table, qualified to be a referee (yes, no) is the response variable and instructional method (individual, group) is the explanatory variable.
Which one of the following tables correctly displays the data from Table 1?

A.

Qualified to be a referee	Instructional method (%)
	Individual	Group
yes (A or B grade)	35	38
no (C, D or E grade)	65	62

B.

Qualified to be a referee	Instructional method (%)
	Individual	Group
yes (A or B grade)	39	38
no (C, D or E grade)	61	62

C.

Qualified to be a referee	Instructional method (%)
	Individual	Group
yes (A or B grade)	39	43
no (C, D or E grade)	61	57

D.

Qualified to be a referee	Instructional method (%)
	Individual	Group
yes (A or B grade)	61	62
no (C, D or E grade)	39	38

E.

Qualified to be a referee	Instructional method (%)
	Individual	Group
yes (A or B grade)	65	57
no (C, D or E grade)	35	43

Use the following information to answer Questions 12–14.

The scatterplot below displays the body length, in centimetres, of 17 crocodiles, plotted against their head length, in centimetres. A least squares line has been fitted to the scatterplot. The explanatory variable is head length.

Question 4 [2022 Exam 1 Q12]

The equation of the least squares line is closest to

• A. \(\textit{head length} = -40 + 7 \times \textit{body length}\)
• B. \(\textit{body length} = -40 + 7 \times \textit{head length}\)
• C. \(\textit{head length} = 168 + 7 \times \textit{body length}\)
• D. \(\textit{body length} = 168 - 40 \times \textit{head length}\)
• E. \(\textit{body length} = 7 + 168 \times \textit{head length}\)

Question 5 [2022 Exam 1 Q13]

The median head length of the 17 crocodiles, in centimetres, is closest to

• A. 49
• B. 51
• C. 54
• D. 300
• E. 345

Question 6 [2022 Exam 1 Q14]

The correlation coefficient \(r\) is equal to 0.963
The percentage of variation in body length that is not explained by the variation in head length is closest to

• A. 0.9%
• B. 3.7%
• C. 7.3%
• D. 92.7%
• E. 96.3%

Question 7 [2022 Exam 1 Q15]

The daily number of cups of coffee sold by a food truck over a three-week period is shown in the table below.

Week	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday
1	123	91	120	176	145	99	187
2	98	104	145	163	134	128	206
3	125	134	128	187	156	102	179

The six-mean smoothed number of cups of coffee, with centring, sold on Thursday in Week 2 is closest to

• A. 127
• B. 138
• C. 147
• D. 155
• E. 163

Question 8 [2022 Exam 1 Q16]

The seasonal index for sales of sunscreen in summer is 1.25
To correct for seasonality, the actual sunscreen sales for summer should be

• A. reduced by 20%
• B. reduced by 25%
• C. reduced by 80%
• D. increased by 20%
• E. increased by 25%