Sound waves from a basketball. Refer to the American Journal of Physics (June 2010) study...

Sound waves from a basketball. Refer to the American Journal of Physics (June 2010) study of sound waves in a spherical cavity, Exercise.

Sound waves from a basketball. Refer to the American Journal of Physics (June 2010) study of sound waves in a spherical cavity, Exercise. The frequencies of sound waves (estimated using a mathematical formula) resulting from the first 24 resonances (echoes) after striking a basketball with a metal rod are reproduced in the following table and saved in the BBALL file. Recall that the researcher expects the sound wave frequency to increase as the number of resonances increases.

Based on Russell, D. A. “Basketballs as spherical acoustic cavities.” American Journal of Physics , Vol. 48, No. 6, June 2010.

a. Hypothesize a model for frequency ( y ) as a function of number of resonances ( x ) that proposes a linearly increasing relationship.

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b. According to the researcher’s theory, will the slope of the line be positive or negative?

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c. Estimate the beta parameters of the model and (if possible) give a practical interpretation of each.

The frequencies of sound waves resulting from the first 24 resonances (echoes) after striking a basketball with a metal rod are saved in the BBALL file. You fit a straight-line model relating frequency ( y ) to number of resonances ( x ) in Above Taken Exercise.

a. Use the model to predict the sound wave frequency for the 10th resonance.

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b. Form a 90% confidence interval for the prediction, part a. Interpret the result.

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c. Suppose you want to predict the sound wave frequency for the 30th resonance. What are the dangers in making this prediction with the fitted model?