Calculation practice: Confidence interval for a mean and one-sample t-testAs the world warms, the geographic ranges of species might shift toward cooler areas. Chen et al. (2011), studied recent changes in the highest elevation at which species occur. Typically, higher elevations are cooler than lower elevations. Below are the changes in highest elevation for 31 taxa, in meters, over the late 1900s and early 2000s. (Many taxa were surveyed, including plants, vertebrates, and arthropods.) Positive numbers indicate upward shifts in elevation, and negative numbers indicate shifts to lower elevations. The values are displayed in the accompanying figure.

a. What is the sample size n?

b. What is the mean of these data points? Remember to give the units.

c. What is the standard deviation of elevational range shift? (Give the units as well.)

d. What is the standard error of the mean for these data?

e. How many degrees of freedom will be associated with a confidence interval and a one-sample t-test for the mean elevation shift?

f. What value of α^α is needed for a 95% confidence interval?

g. What is the critical value of t^t for this α^α and number of degrees of freedom?

h. What assumptions are necessary to use the confidence interval calculations in this chapter?

i. Calculate the 95% confidence interval for the mean using these data.

j. For the one-sample t-test write the appropriate null and alternative hypotheses.

k. Calculate the test statistic t^t for this test.

l. What assumptions are necessary to do a one-sample t-test

m. Describe the P-value for this test as accurately as you can.

n. Did species change their highest elevation on average?

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58.9,58.9, 7.8,7.8, 108.6,108.6, 44.8.44.8, 11.1.11.1, 19.2.19.2, 61.9,61.9, 30.530.5 12.7.12.7, 35.8,35.8, 7.4.7.4, 39.339.3, 24.0,24.0, 62.1,62.1, 24.3.24.3, 55.3 55.3 32.7,32.7, 65.3,65.3, -19.3.-19.3, 7.6.7.6, -5.2, -2.1.-5.2, -2.1, 31.0,31.0, 69.069.0 88.6,88.6, 39.5,39.5, 20.7,20.7, 89.0,89.0, 69.0,69.0, 64.9,64.9, 64.864.8