Question

c. determine the joint frequency for women who watch television using cable and satellite services.
d. list all of the values in the two-way frequency table that are marginal frequencies.

1. skye is a biologist who conducted a study on the abundance of birds on cacao farms in costa rica compared to the abundance of birds in a nearby rainforest. skye used a segmented bar graph, as shown, to display the data for two different species of birds.

a. use the segmented bar graph to complete the two-way frequency table.
table with columns: flycatcher, hummingbird, total; rows: cacao farm, rainforest, total
b. explain using the segmented bar graph or frequency table whether there is an association between a bird’s location and the abundance of birds.

Explanation:

Part a: Completing the Two - Way Frequency Table

Step 1: Analyze the Segmented Bar Graph for Flycatcher in Cacao Farm

From the segmented bar graph, for Flycatcher in Cacao Farm, we can see that the value is 64.

Step 2: Analyze the Segmented Bar Graph for Flycatcher in Rainforest

For Flycatcher in Rainforest, the value is 19.

Step 3: Analyze the Segmented Bar Graph for Hummingbird in Cacao Farm

For Hummingbird in Cacao Farm, the value is 38.

Step 4: Analyze the Segmented Bar Graph for Hummingbird in Rainforest

For Hummingbird in Rainforest, the value is 37.

Step 5: Calculate the Total for Cacao Farm

To find the total number of birds in Cacao Farm, we add the number of Flycatchers and Hummingbirds in Cacao Farm. So, \(64 + 38=102\).

Step 6: Calculate the Total for Rainforest

To find the total number of birds in Rainforest, we add the number of Flycatchers and Hummingbirds in Rainforest. So, \(19+37 = 56\).

Step 7: Calculate the Total for Flycatcher

To find the total number of Flycatchers, we add the number of Flycatchers in Cacao Farm and Rainforest. So, \(64 + 19=83\).

Step 8: Calculate the Total for Hummingbird

To find the total number of Hummingbirds, we add the number of Hummingbirds in Cacao Farm and Rainforest. So, \(38+37 = 75\).

Step 9: Calculate the Grand Total

To find the grand total, we add the total number of birds in Cacao Farm and Rainforest (or the total number of Flycatchers and Hummingbirds). So, \(102 + 56=158\) (or \(83+75 = 158\)).

Now we can fill the two - way frequency table:

	Flycatcher	Hummingbird	Total
Rainforest	19	37	56
Total	83	75	158

Part b: Association between Bird's Location and Abundance

Step 1: Calculate Proportions for Flycatcher

• Proportion of Flycatchers in Cacao Farm: \(\frac{64}{102}\approx0.627\)
• Proportion of Flycatchers in Rainforest: \(\frac{19}{56}\approx0.339\)

Step 2: Calculate Proportions for Hummingbird

• Proportion of Hummingbirds in Cacao Farm: \(\frac{38}{102}\approx0.373\)
• Proportion of Hummingbirds in Rainforest: \(\frac{37}{56}\approx0.661\)

Step 3: Compare Proportions

We can see that the proportion of Flycatchers is higher in Cacao Farm (\(\approx0.627\)) than in Rainforest (\(\approx0.339\)), and the proportion of Hummingbirds is higher in Rainforest (\(\approx0.661\)) than in Cacao Farm (\(\approx0.373\)). Since the proportions of the two bird species differ between the two locations (Cacao Farm and Rainforest), we can conclude that there is an association between a bird's location and the abundance of birds.

Answer:

s

Part a:

The completed two - way frequency table is:

	Flycatcher	Hummingbird	Total
Rainforest	19	37	56
Total	83	75	158

Part b:

There is an association between a bird’s location and the abundance of birds. The proportion of Flycatchers is higher in Cacao farms (\(\frac{64}{102}\approx0.63\)) than in rainforests (\(\frac{19}{56}\approx0.34\)), while the proportion of Hummingbirds is higher in rainforests (\(\frac{37}{56}\approx0.66\)) than in cacao farms (\(\frac{38}{102}\approx0.37\)). Since the species proportions differ by location, there is an association.