Correlation lesson worksheet on snowfall accumulation over time, including data table and graphing space.

Problem Analysis:

The task involves analyzing data related to snowfall accumulation over time during a snowstorm. The data provided includes the total snow accumulation (in cm) at different time intervals (in hours). The goal is to:

1. Draw a scatter plot of the data.
2. Identify the dependent and independent variables.
3. Describe the relationship between the two variables.
4. Describe the correlation between the two variables.

Let's solve each part step by step.

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Part (a): Draw a scatter plot of the data. Be sure to label fully.

#### Step 1: Understand the Data
The data provided is as follows:
- Time (Hours): \(1, 2, 3, 4, 6\)
- Total Accumulation (cm): \(4, 10, 13, 19, 26\)

#### Step 2: Set Up the Scatter Plot
- The horizontal axis (x-axis) represents the Time (Hours).
- The vertical axis (y-axis) represents the Total Accumulation (cm).
- Label both axes clearly.
- Choose appropriate scales for both axes to fit the data points comfortably within the grid.

#### Step 3: Plot the Points
Plot the following points on the scatter plot:
- \((1, 4)\)
- \((2, 10)\)
- \((3, 13)\)
- \((4, 19)\)
- \((6, 26)\)

#### Step 4: Draw the Scatter Plot
Here is a description of how the scatter plot would look:
- The x-axis is labeled "Time (Hours)" and ranges from 0 to 7.
- The y-axis is labeled "Total Accumulation (cm)" and ranges from 0 to 30.
- Each point is plotted accurately based on the given coordinates.

(Although I cannot draw the plot here, you can create it using graph paper or a digital tool.)

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Part (b): Identify the dependent and independent variable and give justification.

#### Step 1: Define Variables
- Independent Variable: This is the variable that is controlled or manipulated. In this case, it is the Time (Hours) because time progresses independently of snowfall.
- Dependent Variable: This is the variable that depends on the independent variable. Here, it is the Total Accumulation (cm) because the amount of snow accumulated depends on the duration of the snowstorm.

#### Step 2: Justification
- The Time (Hours) is the independent variable because it represents the passage of time, which is not influenced by the snowfall itself.
- The Total Accumulation (cm) is the dependent variable because the amount of snow accumulated changes based on how long the snowstorm lasts.

Answer:
- Independent Variable: Time (Hours)
- Dependent Variable: Total Accumulation (cm)

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Part (c): Describe the relationship that exists between the two variables.

#### Step 1: Analyze the Scatter Plot
From the scatter plot (or the data table), observe the trend:
- As time increases, the total accumulation of snow also increases.
- The points appear to follow a general upward trend, indicating a positive relationship.

#### Step 2: Describe the Relationship
The relationship between time and total snow accumulation is positive. As time increases, the total accumulation of snow increases.

Answer:
- As time increases, the total accumulation of snow increases.

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Part (d): Describe the correlation. (Strong/Weak, Positive/Negative)

#### Step 1: Determine the Type of Correlation
- The scatter plot shows a clear upward trend, indicating a positive correlation.
- The points are relatively close to a straight line, suggesting a strong correlation.

#### Step 2: Justify the Strength
- The data points do not deviate significantly from a straight line, indicating that the relationship is consistent and strong.

Answer:
- The correlation is strong and positive.

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Final Answers:

1. Scatter Plot: Drawn with Time (Hours) on the x-axis and Total Accumulation (cm) on the y-axis, plotting the points \((1, 4)\), \((2, 10)\), \((3, 13)\), \((4, 19)\), and \((6, 26)\).
2. Variables:
- Independent Variable: Time (Hours)
- Dependent Variable: Total Accumulation (cm)
3. Relationship: As time increases, the total accumulation of snow increases.
4. Correlation: Strong and positive.

Boxed Final Answer:
\[
\boxed{\text{Strong and positive}}
\]