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QUESTION 1 Four linear models have been developed for a data set. Identify the residual plot that indicates that the developed linear model is justified. (A) (B) ©) (D)
QUESTION 5 Determine the equation of the least-squares line where » =0.926 x =5.2 s = 2.3 y = 68.6 and s =41.7. (A) y=16.79x—-1146.51 (B) y=16.79x-18.70 (C) y=0.05x+68.33 (D) y=0.05x+1.70
QUESTION 8 The following scatterplot shows a linear association between two numerical variables. 30 25 20 y 15 10 Choose the best description for the direction and strength of the association. (A) strong positive (B) strong negative (C) weak positive (D) weak negative
QUESTION 9 It 1s observed that as the number of ice blocks sold each month increases the number of fans sold also increases. Which of these statements is therefore true? (A) (B) ©) (D) There 1s a negative causation between the number of ice blocks sold and the number of fans sold each month. There 1s a positive causation between the number of ice blocks sold and the number of fans sold each month. There 1s a negative association between the number of ice blocks sold and the number of fans sold each month. There 1s a positive association between the number of ice blocks sold and the number of fans sold each month.
QUESTION 14 A sample of university staff and students was asked whether they preferred catching public transport or driving their own car to university. The data collected is shown in the table. Public transport Drive own car What percentage of university students prefer to drive their own car? A) 12% (B) 15% C) 20% (D) 40%
QUESTION 19 (4 marks) Data was collected relating the number of hours spent fishing and the total number of fish caught. The linear model for this data was found to be y = 2.3x + 31.4 where x is the number of hours spent fishing and y is the total number of fish caught. a) Use the model to predict the number of fish caught if 12 hours were spent fishing. [1 mark] b) The correlation coefficient for this data is 0.688 and the coefficient of determination is 0.473. Use each of these to describe the strength of the linear association between the two variables and decide if your prediction is valid. [3 marks]
QUESTION 22 (4 marks) A store asked its junior and senior staff whether or not they would like to change the store uniform. The results are in the frequency table. Change uniform ‘ Do not change uniform Junior staff Senior staff a) Convert the two-way table into a percentaged two-way frequency table using column totals. [2 marks] b) Explain whether there is an association between staff groups and a desire to change the store uniform. [2 marks]
QUESTION 24 (4 marks) The following data for the height of five seedlings was collected and the least-squares line was developed and graphed. 34 30 e 26 2 en 22 = ':g 18 S 14 = 10 i 6 i O 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Time since planting (days) a) Use the least-squares line to estimate the height of a nine-day-old seedling. [1 mark] b) Classify the prediction for 24a) as either interpolation or extrapolation. [1 mark] c) Based on the graph the following statement was made: ‘A seedling will reach a height of about 32 cm by day 29. Comment on the reasonableness and the possible dangers of this statement. [2 marks]
QUESTION 2 (5 marks) The number of people living in each household and the average daily household water usage measured in litres (L) were recorded for 10 households. Number of people average dailyhousehold 160 | 320 | 480 | 410 | 280 | 240 | 130 | 940 | 1340 water usage (L) Calculate Pearson’s correlation coefficient and then evaluate the appropriateness of using this coefficient for the association between daily water usage and the number of people living in a household. 1400 1200 1000 800 600 400 200 Average daily household water usage (L) 0 1 2 3 4 5 6 7 8 Number of people in each household
QUESTION 3 (6 marks) The least-squares line for a sample of five data points was found to be y = 2.1875x + 0.0625 with a correlation coefficient of » = 0.875. Determine a set of values for p and ¢ given that these values differ by 3.
QUESTION 3 The table shows the results of a student survey about their preferred movie genre. 2 Of the students who preferred comedy what percentage were in Year 9 or higher? (A) 25% (B) 30% (C) 60% (D) 75%
QUESTION 4 A confounding variable is a variable that (A) can only take on a certain number of values. (B) remains constant throughout a statistical investigation. (C) 1s used to predict a difference in the response variable. (D) other than the explanatory variable influences the response variable.
QUESTION 6 These scatterplots show the number of high-rises in a city and their distance from the city centre. Which scatterplot was used to extrapolate that 25 km from the city centre there were 20 high-rises? (A) ©) 250 p— S O Number of high-rises N O - 250 Number of high-rises o O N O == 0 5 10 15 20 25 Distance from city centre (km) \ y=-5x+ 160 0 5 Distance from city centre (km) 10 15 20 25 (D) Number of high-rises Number of high-rises p— S S N S S 250 p— S S N S S 0 5 10 15 20 25 Distance from city centre (km) y=-3.75x+ 100 0 5 Distance from city centre (km) 10 15 20 25
QUESTION 11 Which option is an example of bivariate data? (A) (B) ©) (D) The rating given to a brand of meat pies as poor fair or good. The number of people in a household and amount of water used. The number of cars passing through a particular set of traffic lights. The time a person spends using a mobile phone on a Friday evening.
QUESTION 16 (4 marks) The table shows the values of bivariate data with variables g and 4. a) Construct a scatterplot of the data with g as the explanatory variable. [2 marks] 11 10 0 1 2 3 4 5 6 7 8 9 10 11 b) Describe the association in terms of form and strength. [2 marks]
QUESTION 18 (4 marks) The table shows the profit made each year (in thousands of dollars) by a small business. a) Use a mathematical model to determine the equation of the least-squares line to fit this data. [2 marks] b) Use the least-squares line to forecast the profit in 2021 to the nearest hundred dollars. [2 marks]
QUESTION 5 (6 marks) Researchers gathered a set of data to determine if a model could reliably predict systolic blood pressure given a person’s age. One candidate was 31 years old and had a systolic blood pressure of 119. For this data the correlation coefficient () 1s 0.875 the standard deviation for the person’s age (Sx) is 4 and the standard deviation for the systolic blood pressure (s y) is 6. A residual plot was produced for the model. 7.5 Age Residual (actual — predicted) (e Determine the actual systolic blood pressure to the nearest whole number for the oldest person in the sample (40 years old).
QUESTION 8 The scatterplot shows the annual number of visitors to the Great Barrier Reef Marine Park. Visitor number (millions) 3.5 0.5 0 2010 2011 20 12 2013 2014 2015 Year For 2018 the annual number of visitors could best be (A) 1nterpolated as 2.7 million. (B) extrapolated as 2.7 million. ©) interpolated as 3.2 million. (D) extrapolated as 3.2 million. 2016 2017 2018 20 19 2020
QUESTION 10 Which example states an explanatory variable followed by a response variable? (A) car manufacturers and car colours (B) dog breeds and frequency of names (C) plant growth and amount of fertiliser used (D) daily temperatures and daily ice cream sales
QUESTION 11 The equation of a fitted line for the number of free throws in basketball ¢z and the number of hours in a training session 4 18t =26.781 + 12.974 h The predicted number of free throws for a 5-hour training session when rounded to the nearest whole number is (A) 64 (B) 65 (©) 91 (D) 92
QUESTION 12 Identify the scatterplot that best demonstrates a strong negative association. A) (B) o'.. o'.. o'.. o... o... C) & (D) ° ‘: .. ° o . o o e o “o ° ° > 3o 0o ©® o oo ° % Y : ..0 ..O ° o
QUESTION 13 The two-way table summarises the semester 1 results for students enrolled in two courses Machinery and Electrical. Students achieved either satisfactory (S) or unsatisfactory (U). Machinery S U The 10% cell in the table indicates that (A) 10% of all students achieved satisfactory in Electrical. Electrical (B) 10% of all students achieved unsatisfactory in Machinery. (C) 10% of the students who achieved satisfactory in Electrical achieved unsatisfactory in Machinery. (D) 10% of the students who achieved unsatisfactory in Machinery achieved satisfactory in Electrical.
QUESTION 16 (3 marks) The table shows the number of sales for a small business in their first six months of trading. 4 226 240 335 a) Use your calculator to determine the equation of the least-squares line. [1 mark] b) Use the equation from Question 16a) to predict the number of sales in the 21st month. [2 marks]
QUESTION 19 (4 marks) The graph shows the amount of rainfall (in mm) for each quarter from 2016 to 2021. 250 200 e g = 150 g s (2 o = 100 o £ < 50 O i | | | i ' | i | | | | | i | | | i 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 | | | ] L 1 2016 2017 2018 2019 2020 2021 Quarters (each year) a) Describe the long-term trend and seasonality of the time series data. [2 marks] b) A least-squares line was fitted to the data with y representing the amount of rainfall and x representing the number of quarters since the beginning of 2016 (e.g. x = 5 for the first quarter of 2017). y=1.763x+ 156.5 Interpret the y-intercept and slope of the fitted line. [2 marks]
QUESTION 23 (4 marks) The least-squares line has been provided for a scatterplot that shows the association between an employee’s years of experience n and their hourly pay p. 60 50 » 40 3 > 30 5 S = 20 10 0 2 4 6 8 10 12 Years of experience a) Given that the least-squares line passes directly through the points (2 20) and (7 40) determine its equation. [2 marks] b) Use the equation from Question 23a) to predict the hourly pay of an employee with 15 years experience. [2 marks]
QUESTION 24 (5 marks) The maximum temperature and the number of pies sold each day at a bakery are provided in the table. Maximum e [ [ [ » [ [ [ ] a) Construct a scatterplot to display the data on the grid provided. [3 marks] b) Describe the association between the maximum temperature and the number of pies sold in terms of direction and strength. [2 marks]
QUESTION 3 (5 marks) In a company’s first 10 years of operation the average annual profit (y) was $9660 with a standard deviation (s ) of $3010. Fitting a least-squares line to the data comparing annual profit (») to the year of operation (x) produced a correlation coefficient of 0.9987. Show that the predicted profit to the nearest dollar for this company in the 11th year of operation will be $15121.
QUESTION 1 A linear association with a correlation coefficient of 0.23 is best described as (A) weak positive. (B) weak negative. (C) strong positive. (D) strong negative.
QUESTION 4 Athletes were surveyed about their preferred shoe brand: X Y or Z. The results are shown in the frequency table. mw | | | | The percentage of field athletes who prefer brand Y is (A) 12% (B) 15% (C) 30% (D) 40%
QUESTION 5 A scatterplot is created to identify the nature of the relationship between two variables: vehicle age and distance travelled. Which statement is correct? (A) The vertical axis should show vehicle age as the response variable. (B) The horizontal axis should show vehicle age as the explanatory variable. (C) The horizontal axis should show distance travelled as the response variable. (D) The vertical axis should show distance travelled as the explanatory variable.
QUESTION 7 Which statement is always true for a causal relationship between an explanatory variable and a response variable? (A) (B) (C) (D) One of the variables is a confounding variable. The relationship is explained by a third variable. There is a positive association between the variables. The response variable is dependent on the explanatory variable.
QUESTION 14 A calculator is used to determine the equation of the least-squares line for the plant growth data in the table. What is the correct equation? (A) d=0.6h+5.7 (B) h=0.6d+5.7 (C) d=5.7h+0.6 (D) h=5.7d+0.6
QUESTION 22 (4 marks) A person used a fitness tracker to monitor their hours of sleep and the distance they travelled each day. Sleep (hours) Distance (km) a) Using distance as the response variable display the data in a scatterplot with labelled axes. [3 marks] a a a a b) Identify the direction of the association between hours of sleep and distance travelled. [1 mark]
QUESTION 4 (5 marks) Hiroki believes that more fish are caught on warmer days. Jiro believes that the number of fish caught in a day is more dependent on the number of people fishing. Bivariate datasets for six days are shown. Temperature ¢ (°C) Number of fish caught f Calculate the correlation coefficient for each dataset and use the results to identify the explanatory variable for the stronger linear association. Use the least-squares line equation for the stronger linear association to predict the number of fish caught on a 25 °C day when 50 people are fishing.
QUESTION 6 (7 marks) The table shows the average superannuation account balance for workers of various ages in two different industries. The coefficient of determination R? for age versus account balance is 0.95 for industry A and 0.96 for industry B. 40-year-old Leigh works in the industry for which age explains a higher percentage of the account balance variation. Tony is 10 years older than Leigh and works in the other industry. Account balance ($) Age (years) Industry A Industry B 42.000 60.000 Use linear models to predict the difference in current superannuation account balances for Leigh and Tony.
QUESTION 5 Bivariate data involves (A) two values. (B) two variables. (C) two data displays. (D) two data varieties.
QUESTION 11 Two variables are displayed on a scatterplot. Which statement below is correct? (A) Only if there 1s a causal relationship between the two variables will they have a positive association. (B) Ifthe two variables have a negative association then there is not a causal relationship between the two variables. (C) [Ifthe two variables are associated either positively or negatively then there could be a causal relationship between the two variables. (D) Ifthe two variables are associated either positively or negatively then there is definitely a causal relationship between the two variables.
QUESTION 23 (6 marks) The number of meals sold (y) by a restaurant each month (x) for the first six months of business is shown on the scatterplot below. The line of best fit its equation and the coefficient of determination (R?) are also shown. Number of meals Month The restaurant was closed for renovations for most of one month. a) Identify the number of meals sold in that month. [1 mark] b) Describe the effect that this outlier has on the coefficient of determination. [1 mark] c) Use the line of best fit to predict the number of meals that will be sold in the 18th month of the business operation. [2 marks] d) Evaluate the reasonableness of your solution for 23c). [2 marks]
QUESTION 24 (4 marks) Students were surveyed regarding their attitudes towards dancing and swimming. The resulting data is displayed in the table below. Enjoy dancing Do not enjoy dancing Enjoy swimming Do not enjoy swimming a) b) ©) Calculate how many students enjoy swimming [1 mark] Calculate how many students were surveyed. [1 mark] Calculate the percentage of students who enjoy both activities. Express your answer correct to two decimal places. [2 marks]
QUESTION 26 (2 marks) The number of students (s) and the number of computers (c) in four secondary schools in Queensland are shown in the table below. Number of students (s) Number of computers (c) 348 307 507 427 798 671 1202 986 a) Identify the response variable. [1 mark] b) Determine a linear relationship for this data by fitting a least-squares line to the data. [1 mark]
QUESTION 3 (4 marks) Music students in a school were asked how many hours they practised their musical instrument each week. Seventy-two Year 7 music students were surveyed. The results are shown below. 15 students practised for 2 hours or less. 53 students practised for more than 2 hours and up to 4 hours. 4 students practised for more than 4 hours per week. Seventeen Year 12 music students were surveyed. The results are shown below. 2 students practised for 2 hours or less. 11 students practised for more than 2 hours and up to 4 hours. * 4 students practised for more than 4 hours per week. Determine any patterns that suggest the presence of an association providing reasons for your conclusion.
QUESTION 8 (3 marks) A teacher wants to know the best way for their students to improve their marks. They surveyed a sample of students who graduated last year and asked them three questions: « What was the overall mark you achieved on the final assessment? * On a typical night how many hours sleep would you get? * During a typical school term how many classes did you miss? They obtained the following data: Overall percentage mark (%) Construct a mathematical argument to determine which explanatory variable is the better predictor for the overall mark.
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