Test the hypothesis that the average running time of films use as a guide only

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  1. Let X ? uniform (0, ?) and consider testing H0: ? 1 vs. H1: ? 1. We take one observation, X, from this distribution and reject H0 if X 0.9.

(a) Find ?, the type I error probability.

(b) Suppose that ? 1.1. Find ?, the type II error probability.

  1. Let X1,..., Xn ?N(?, 4). To test H0: ?10 vs H0: ?10 we take a random sample of size n 16 and reject the null hypothesis if 14.

(a) Find ?, the type I error probability.

(b) Suppose that ? 11. Find ?, the type II error probability.

  1. A soft-drink machine at a steak house is regulated so that the amount of drink dispensed is approximately normally distributed with a mean of 200 milliliters.

(a) State the null and alternative hypotheses if we wish to check if the machine is calibrated correctly.

H0: 200 ...

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