Question

1. Pierce (1949) measured the chirping frequency (chirps/sec) of crickets kept at varying temperatures to determine if chirp frequency varies as a function of temperature. He collected the data in Table 1, but he forgot to convert degrees F to C. He needs you to convert them to ^oC using the equation ^oC = 5/9[^oF -32^o] and the Transform/Compute command in SPSS. What type of test do you think he needed to run? Decide which test is most appropriate, use the SPSS tutorial for the appropriate test (on D2L), and answer the following questions.

1a.       What test would you use to answer this question, and why?

1b.       Is chirp frequency affected by temperature (^oC)? What portion of total variation in chirp frequency is attributable to temperature?

1c.       What is the expected increase in chirps/second for each degree Centigrade increase in temperature?

1d.       Is there a linear equation? If so, what is the linear equation?

1e.      If you recorded a cricket chirping at 20 chirps per second, what would be the predicted temperature?

1f.        Produce the appropriate figure

Table 1. Chirp Data

Chirp Frequency	Temp (F)
20	88.6
16	71.6
19.8	93.3
18.4	84.3
17.1	80.6
15.5	75.2
14.7	69.7
17.1	82
15.4	69.4
16.2	83.3
15	78.6
17.2	82.6
16	80.6
17	83.5
14.1	76.3

Answer 1

1a.       What test would you use to answer this question, and why?

Linear regression

1b.       Is chirp frequency affected by temperature (oC)? What portion of total variation in chirp frequency is attributable to temperature?

Using Excel

data -> data analysis -> regression

p-value = 0.0001 < alpha

hence we reject the null hypothesis

we conclude that there is evidence chirp frequency is affected by temperature

R^2 = 0.6997

hence 69.97 % of variation is in chirp frequency is attributable to temperature

1c.       What is the expected increase in chirps/second for each degree Centigrade increase in temperature?

slope = 0.3882

1d.       Is there a linear equation? If so, what is the linear equation?

y^ = 6.2865 + 3.8822 Temp(C)

1e.      If you recorded a cricket chirping at 20 chirps per second, what would be the predicted temperature?

20=6.2865+0.3882 * Temp

solving Temp = 35.3259

1f

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