1. In a sample of 400 ball bearings, the correlation coefficient between eccentricity and smoothness was r = 0.10.

a. Find the P-value for testing H0 : ρ ≤ 0 versus H1 : ρ> 0. Can you conclude that ρ> 0?

b. Does the result in part (a) allow you to conclude that there is a strong correlation between eccentricity and
smoothness? Explain.

2. The article " ‘Little Ice Age' Proxy Glacier Mall Balance Records Reconstructed from Tree Rings in the Mt. Wadding- ton Area, British Columbia Coast Mountains, Canada" (S. Larocque and D. Smith, The Holocene, 2005:748-757) evaluates the use of tree ring widths to estimate changes in the masses of glaciers. For the Sentinel glacier, the net mass balance (change in mass between the end of one summer and the end of the next summer) was measured for 23 years. During the same time period, the tree-ring index for white bark pine trees was measured, and the sample correlation between net mass balance and tree ring index was r = -0.509. Can you conclude that the population correlation ρ differs from 0?