Year 11 General Maths - Chapter 7 Test 1 - Bivariate Data

For which of the following pairs of variables would it be appropriate to construct a scatterplot:

• Height (tall, average short) and weight (heavy average, light)

• Political affiliation (Labor, Liberal, Other) and years of education.

• Age in years and weight in kg

• Height in cm and gender (male, female).

• Score out of 50 on a test for a group of males and a group of females

The following plot shows the number of salespeople in each region and the number of sales recorded for the region by a company. From the scatterplot, it can be said that:

• There is no association between the variables

• There is a weak positive association between the variables

• There is a weak negative association between the variables.

• There is a strong positive association between the variables

• There is a strong negative association between the variables.

A correlation coefficient of –0.65 would describe a relationship classified as:

• weak negative

• weak positive

• moderate negative

• strong negative

• no relationship

There is a strong positive correlation (r = 0.985) between the level of carbon monoxide emissions and the level of traffic congestion in a city From this information, we can conclude that:

• the level of carbon monoxide emissions in a city will increase if the traffic congestion in a city is increased

• the level of carbon monoxide emissions in a city will decrease if the traffic congestion is increased

• cities with a high level of carbon monoxide emissions tend to have high traffic congestion

• cities with a high level of carbon monoxide emissions tend to have low levels of traffic congestion

• increasing the carbon emissions in a city will increase the traffic congestion

In the regression line  $y=-10+3x$  

• The y-intercept = 0 and the slope = 3.

• The y-intercept = –10 and the slope = 3.

• The y-intercept = 3 and the slope = –10.

• The y-intercept = –10 and the slope = –3.

• The y-intercept = 10 and the slope = 3.

A regression line has been fitted to the following scatterplot. The equation of the line is closest to:

• $y=–1.3+1.1x$

• $x=–1.3+1.1y$

• $y=1.1–1.3x$

• $y=1.1+0.9x$

• $y=0.9+1.1x$

Suppose that the least squares regression line which would enable the amount of money spent at the shopping centre (in dollars) to be predicted from the number of hours spent at the shopping centre is given by:
 $Money\ spent=20+50\times Hours\ spent\ shopping$ 
Using this rule, the expenditure on shopping by an individual who spends three hours at the shopping centre is predicted to be:

• $50

• $70

• $150

• $170

• $210

Suppose that the least squares regression line which would enable the amount of money spent at the shopping centre (in dollars) to be predicted from the number of hours spent at the shopping centre is given by: 
 $Money\ spent=20+50\times Hours\ spent\ shopping$ 
The slope of the line can be interpreted as follows:

• On average, for each extra hour spent shopping an extra $50 is spent

• On average, for each extra 50 minutes spent shopping an extra $1 is spent.

• On average, customers spend $20 per hour at the shopping centre.

• On average, customers spend $50 at the shopping centre.

• On average, customers will spend more per hour the longer they stay at the shopping centre

The value of the correlation coefficient  $r$   is useful indicator of the strength of an association between two variables when:

• one variable is numerical and the other is nominal.

• both variables are categorical

• both variables are numerical and the association is linear. 

• one variable is numerical and the other ordinal. 

• none of the above. 

The production costs ($C) of a company which manufactures a particular computer game is related to the number of games produced (N) as follows:
 $C=12000+35N$  
From this equation we can say that, on average: 

• Cost of production increases at a rate of $12 000 per unit. 

• Cost of production increases at a rate of $N per unit. 

• Cost of production increases at a rate of $35 per unit. 

• Cost of production is fixed at $12 000. 

• Cost of production decreases as the number of units produced increases