Question

the table below includes data from taxi rides. the distances are in miles, the times are in minutes, the fares are in dollars, and the tips are in dollars. is there sufficient evidence to conclude that there is a linear correlation between the time and the tip amount? construct a scatterplot, find the value of the linear correlation coefficient r, and find the p - value of r. determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. use a significance level of α = 0.01. does it appear that riders base their tips on the time of the ride? click here for information on the taxi rides. construct a scatterplot. choose the correct graph below. determine the linear correlation coefficient. the linear correlation coefficient is r = (round to three decimal places as needed.)

Explanation:

To determine the linear correlation coefficient \( r \) and analyze the relationship between ride time (minutes) and tip amount (\$), we typically use statistical software or a calculator with correlation capabilities. However, since the data points are not fully visible, we'll assume a general approach:

Step 1: Identify Variables

Let \( x \) = Ride Time (minutes) and \( y \) = Tip Amount (\$).

Step 2: Calculate Correlation Coefficient \( r \)

Using the formula for Pearson's correlation coefficient:

$$ r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}} $$

where \( n \) is the number of data points.

Step 3: Interpret \( r \)

• If \( r \approx 0 \), no linear correlation.
• If \( |r| \) is close to 1, strong linear correlation.

Assuming typical taxi data (longer rides might correlate with higher tips, but tips also depend on service), let’s estimate. For example, if data shows a weak positive correlation, \( r \approx 0.2 \) (but this is speculative without full data).

Final Answer (Estimated, pending full data):

The linear correlation coefficient \( r \approx \boldsymbol{0.20} \) (rounded to two decimal places; actual value depends on data).

(Note: For precise calculation, use software like Excel, TI-84, or statistical tools with the provided data points.)

Answer:

To determine the linear correlation coefficient \( r \) and analyze the relationship between ride time (minutes) and tip amount (\$), we typically use statistical software or a calculator with correlation capabilities. However, since the data points are not fully visible, we'll assume a general approach:

Step 1: Identify Variables

Let \( x \) = Ride Time (minutes) and \( y \) = Tip Amount (\$).

Step 2: Calculate Correlation Coefficient \( r \)

Using the formula for Pearson's correlation coefficient:

$$ r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}} $$

where \( n \) is the number of data points.

Step 3: Interpret \( r \)

• If \( r \approx 0 \), no linear correlation.
• If \( |r| \) is close to 1, strong linear correlation.

Assuming typical taxi data (longer rides might correlate with higher tips, but tips also depend on service), let’s estimate. For example, if data shows a weak positive correlation, \( r \approx 0.2 \) (but this is speculative without full data).

Final Answer (Estimated, pending full data):

The linear correlation coefficient \( r \approx \boldsymbol{0.20} \) (rounded to two decimal places; actual value depends on data).

(Note: For precise calculation, use software like Excel, TI-84, or statistical tools with the provided data points.)