Calculation practice: Standard error and hypothesis testing for a correlation. Refer to Practice Problem 1. Test whether there is a correlation in the population between giggle fundamental frequency and age.

a. State the null and alternative hypotheses.

b. Calculate the standard error of the sample correlation r^r .

c. Calculate the t-statistic.

d. What is the sample size? What are the degrees of freedom?

e. Obtain the critical value for t corresponding to α=0.05.

f. What is the conclusion from the test?

Data from problem  1.

Calculation practice. Estimate a correlation coefficient. In their study of hyena laughter, or “giggling” (see Chapter 12, Assignment Problem 24), Mathevon et al. (2010) asked whether sound spectral properties of hyenas’ giggles are associated with age. The accompanying figure and data show the giggle fundamental frequency (in hertz) and the age (in years) of 16 hyenas. What is the correlation coefficient in the data, and what is the most-plausible range of values for the population correlation?

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Fundamental frequency (Hz) 900- 800- 700- 600- 500- 400- 300- 0 5 10 Age (years) 15 20