To determine if the sample data comes from an approximately normal population, we can create a histogram or a box plot. Unfortunately, as a text-based AI, I'm unable to create graphical content. However, I can guide you through the steps to create a histogram or box plot using software like Excel, R, or Python.
Steps to Create a Histogram in Excel:
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Input the Data:
- Open Excel and enter the data:
108, 112, 117, 130, 111, 131, 113, 113, 105, 128in a single column.
- Open Excel and enter the data:
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Create the Histogram:
- Highlight the data.
- Go to the "Insert" tab.
- Click on "Insert Statistic Chart" and select "Histogram."
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Adjust the Histogram:
- You can adjust the bin width, axis titles, and chart title to make the histogram clearer.
Steps to Create a Box Plot in Excel:
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Input the Data:
- The same as above, load your data into a single column.
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Create a Box Plot:
- Highlight the data.
- Go to the "Insert" tab.
- Click on "Insert Statistic Chart" and select "Box and Whisker."
Steps to Create a Histogram in Python:
import matplotlib.pyplot as plt
# Data
data = [108, 112, 117, 130, 111, 131, 113, 113, 105, 128]
# Create Histogram
plt.hist(data, bins=5, edgecolor='black', alpha=0.7)
plt.title('Histogram of Wasted Time')
plt.xlabel('Minutes Wasted')
plt.ylabel('Frequency')
plt.show()
Steps to Create a Box Plot in R:
# Data
data <- c(108, 112, 117, 130, 111, 131, 113, 113, 105, 128)
# Create Box Plot
boxplot(data, main="Box Plot of Wasted Time", ylab="Minutes Wasted")
Interpreting the Graphs:
- Histogram: Look for a bell-shaped curve. The more the distribution resembles this shape, the more normalized it is.
- Box Plot: Check for symmetry around the median. If the whiskers are of similar length, and there are no significant outliers, the population can be considered approximately normal.
After you create and inspect the graph, you will be able to assess whether the data likely comes from an approximately normal population.
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