The ability of ecologists to identify regions of greatest species richness could have an impact on the preservation of genetic diversity, a major objective of the World Conservation Strategy. A study used a sample of n = 33 lakes to obtain the estimated regression equation

y = 3.89 + 0.033x1 + 0.024x2 + 0.023x3 ? 0.0080x4 ? 0.13x5 ? 0.72x6

where y = species richness, x1 = watershed area, x2 = shore width, x3 = poor drainage (%), x4 = water color (total color units), x5 = sand (%), and x6 = alkalinity.

The coefficient of multiple determination was reported as R2 = 0.87. Carry out a test of model utility. State the appropriate hypotheses.( 4 choices )

H0: ?1 = ?1 = ... = ?6 = 0

Ha: no ?i = 0

H0: ?1 = ?1 = ... = ?6 = 0

Ha: at least one among ?1, ..., ?6 is not zero

H0: ?1 ? ?1 ? ... ? ?6 ? 0 Ha: ?1 = ?1 = ... = ?6 = 0 H0: ?1 ? ?1 ? ... ? ?6 ? 0

Ha: at least one among ?1, ..., ?6 is zero

State the rejection region and compute the test statistic value. Use ? = 0.05. Round your answers to two decimal places. rejection region f ? test statistic f = State the conclusion in the problem context.(4 choices)

Reject H0. The model is judged not useful.

Fail to reject H0. The model is judged not useful.

Fail to reject H0. The model is judged useful.

Reject H0. The model is judged useful.