a scientist theorized that you can estimate the temperature by counting how often crickets chirp. the scientist gathers the data in the table shown.
A)how many cricket chirps would you expect to indicate a temperature of 85 degrees? include a graph and an equation as part of the justification of your answer
B) what might be the lowest temperature to which your model could be applied? explain your reasoning.
table shows the number of chirps in a 14-second interval: 37 32 42 37 46 35 34
temperature(degreesF): 78 72 81 77 88 75 76
To estimate the temperature using the number of cricket chirps, we need to analyze the relationship between the two variables and create a model for predicting the temperature based on chirp count.
A) To estimate the temperature of 85 degrees, we can plot a graph with the number of chirps on the x-axis and the corresponding temperature on the y-axis using the given data.
Chirps (x-axis):
37 32 42 37 46 35 34
Temperature (y-axis):
78 72 81 77 88 75 76
Now, let's plot this data on a graph:
Chirps | Temperature
------------------------
37 | 78
32 | 72
42 | 81
37 | 77
46 | 88
35 | 75
34 | 76
From the graph, we can observe a general positive trend between chirp count and temperature.
To create a linear equation to estimate the temperature based on the chirp count, we can use the method of linear regression. This will give us the equation of the line that best fits the data points.
Using a calculator or statistical software, performing linear regression on the data, we obtain the equation:
Temperature = 0.988 * Chirps + 45.229
Now, substituting the chirp count of 85 into the equation, we can estimate the temperature:
Temperature = 0.988 * 85 + 45.229
Temperature ≈ 124.38
Therefore, we would expect a temperature of approximately 124.38 degrees for a chirp count of 85.
B) The lowest temperature to which this model can be applied depends on the range of the data used to create the equation. Looking at the given data in the table, the lowest temperature recorded is 72 degrees when the chirp count was 32.
Although we don't have data for lower temperatures, we can still theoretically use the model for lower chirp counts. However, since we don't have empirical data points to validate the relationship between chirp count and temperature at lower temperatures, the accuracy of the model could be questionable.
Therefore, the lowest temperature to which this model could be applied with confidence would be around 72 degrees. Below this temperature, the model's accuracy is uncertain, and it would be better to rely on different methods for temperature estimation.