Crickets make their chirping sounds by rapidly sliding one wing over the other. The faster they move their wings, the higher the chirping sound that is produced. Scientists have noticed that crickets move their wings faster in warm temperatures than in cold temperatures. Therefore, by listening to the pitch of the chirp of crickets, it is possible to approximate the temperature of the air. Pierce summarized the recorded pitch (in vibrations per second) of a cricket chirping recorded at 15 temperatures. Chirps Per Second 20 16 20 18 17 16 15 17 15 16 15 17 16 17 14
Temperature 89 72 93 84 81 75 70 82 69 83 80 83 81 84 76
Is there a relationship between crickets chirps and temperature?
Create a well-labelled scatterplot and comment on whether the relationship between the two variables appears linear.
Use your calculator to compute the linear correlation coefficient r9sXHPj+akPGqWzgMx31pN8gTqA4PYEoEKQ FgQAS4 and decide whether a significant linear relationship exists between the variables.
Justify your choice using Table A-5 from the text with a 0.051c7j7wtNZsnditY4uumzX1VgmhOg2pl Qi8JgKh6r level of significance. (If your computed value of r9sXHPj+akPGqWzgMx31pN8gTqA4PYEoEKQ FgQAS4 is greater than the critical value given in the table, conclude that there is a significant linear relationship between the variables).
State the null and alternative hypothesis to test for linear correlation. Use your calculator to find the p-value of the test. How does your p-value support the conclusion reached in part (a)?