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Suppose that X1, . . . , Xn comprise a random sample from the normal distribution with unknown mean ? and variance 1. Suppose that it is desired to test the same hypotheses as in Exercise 3. This time, however, the test procedure ? will be chosen so that 19?(0|?) = 1? ?(0.5|?).
a. Find the value cn so that the test procedure ? rejects H0 if n ? cn for each value n = 1, n = 100, and n = 10,000.
b. For each value of n in part (a), find the size of the test procedure ?.
A Carnot heat pump is used to heat and maintain a residential building at 75°F. An energy analysis of the house reveals that it loses heat at a rate of 2500 Btu/h per °F temperature difference between the indoors and the outdoors. For an outdoor temperature of 35°F, determine
(a) The coefficient of performance and
(b) The required power input to the heat pump.
