Question

A scientist investigated the relationship between the weight of a toy boat and the time it took for the boat to float 100 ft down a stream which was moving at a constant speed. The wind current above the stream was blowing at a constant speed in the opposite direction of the stream. The scientist recorded the experimental data in a table. Weight (oz) 10 12 14 16 18 20 22 Time (s) 23 22.7 22.3 21.6 21.4 21.1 20.7 (a) Describe the relationship between the weight of the boat and the time it took to float 100 ft down the stream. Is there a positive or negative correlation between the two variables? How do you know? (b) What is the numeric value of the correlation coefficient to the nearest hundredth? Interpret its meaning. (c) Consider the context of the situation. Is the correlation between weight and time likely due to causation? Justify your answer.

Answer 1

Answer:

See below

Step-by-step explanation:

Lets assume weight is input and time is output

The function based on the input and output values is close to linear and it is decreasing (graph is attached)

Answers are

• a) correlation is negative as time decreases with increase in weight.
• b) Numeric value is obtained -0.99 by using the formula attached as picture.  It is 'very strong negative relationship'
• c) Yes. Because weigh increase causes time to decrease