**Problem:**

(a) Differentiate between linear and log-linear model.

(b) Distinguish between type I and type II errors.

(c) (i) A bulb manufacturer claims that its bulbs last 36000 hours, on average. A consumer believes that it is actually less and plans to test this by assessing the lifetime of bulbs on a sample of 35 bulbs and tests these assumptions at significance level of 0.05. If the standard deviation of bulb life is 4000 hours, what is the probability of a type II error if the actual mean lifetime of the bulb is 33000 hours?

(ii) Given that the significance level is 0.005, what is the probability of a type II error if the actual mean lifetime of the bulb is 32500 hours?

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