Question: The random variable X is normally distributed with unknown mean p and known variance a2 = 225. A sample of size N = 9 from

The random variable X is normally distributed with unknown mean p and known variance a2 = 225. A sample of size N = 9 from X is observed, with the sample values 42, 56, 68, 56, 48, 36, 45, 71, and 64.

(a) Compute the sample mean and sample variance.

(b) Name three intuitively reasonable point estimators for p, and determine the corresponding estimates from the above data.

(c) Which of the three estimators given in

(b) would you prefer? Why?

(d) Find an 80 percent confidence interval for p.

(e) Find a 95 percent confidence interval for p.

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