An engineer found that by adding small amounts of a compound to rechargeable batteries during manufacture, she could extend their lifetimes. She experimented with different amounts of the additive ( g) and measured the hours they lasted in a laptop.

(a) Calculate the least squares estimates β̂₀ and β̂₁. Also estimate the error variance σ².
(b) Test H₀ : β̂₁ = l versus H₁ : β̂₁ ≠ 1 with α = .05.
(c) Estimate the expected y value corresponding to x = 3.5 and give a 95% confidence interval. Interpret.
(d) Construct a 90% confidence interval for the intercept β̂₀. Interpret.

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Amount of Additive 0 1234 4 Life (hours) 3.9 4.0 4.5 4.6 5.0