IA 2 Retrieval Rehearsal – Term 1 Week 4

Calculate how many students enjoy swimming.

Answer explanation

To find how many students enjoy swimming, count the number of students who indicated swimming as their preferred activity in the survey. This total gives the exact number of students who enjoy swimming.

Calculate how many students were surveyed.

Answer explanation

To find the number of students surveyed, sum the responses from each group or category provided in the data. The total will give the exact number of students who participated in the survey.

Calculate the percentage of students who enjoy both activities. Express your answer correct to two decimal places.

Answer explanation

To find the percentage of students who enjoy both activities, divide the number of students who enjoy both by the total number of students, then multiply by 100. Round the result to two decimal places for the final answer.

A scatterplot is created to identify the nature of the relationship between two variables: vehicle age and distance travelled.

Which statement is correct?

• The vertical axis should show vehicle age as the response variable.

• The horizontal axis should show vehicle age as the explanatory variable.

• The horizontal axis should show distance travelled as the response variable.

• The vertical axis should show distance travelled as the explanatory variable.

Answer explanation

In a scatterplot, the explanatory variable is typically placed on the horizontal axis. Here, vehicle age is the explanatory variable, while distance travelled is the response variable, which should be on the vertical axis.

Four linear models have been developed for a data set. Identify the residual plot that indicates that the developed linear model is appropriate.

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Answer explanation

There is no clear pattern and the points are spread evenly about the x-axis.

The approximate coordinates of Geelong, Australia, are 38°09′ S, 144°21′ E and Kushiro, Japan, are 43°01′ N, 144°21′ E.

Calculate the distance between Geelong and Kushiro to the nearest kilometre.

• 9026km

• 9099km

• 546km

• 541km

Answer explanation

To calculate the distance between Geelong and Kushiro, we can use the great circle formula. This is 111.2 x angular distance. The angular distance is determined by adding their latitudes as they are in different hemispheres. Given their coordinates, the distance is approximately 9026 km, making this the correct choice.

City A is located at 55° N, 120° E and City B is located at 40° N, 165° E. The sun will rise in City A approximately

• 1 hour before it rises in City B.

• 1 hour after it rises in City B.

• 3 hours before it rises in City B.

• 3 hours after it rises in City B.

Answer explanation

City A (120° E) is further west than City B (165° E), and the difference in longitude (45°) means City A experiences sunrise later. Therefore, the sun rises in City A approximately 3 hours after it rises in City B.

Given the following set of paired data points, calculate the Pearson correlation coefficient (r) and interpret its value to determine the strength and direction of the linear relationship between the two variables.

Answer explanation

Calculate r using stats mode on your calculator. A value close to 1 indicates a strong positive correlation, while a value close to -1 indicates a strong negative correlation.