13.46 The article “Performance Test Conducted for a Gas Air-Conditioning System” (American Society of Heating, Refrigerating, and Air Conditioning Engineering

[1969]: 54) reported the following data on maximum outdoor temperature (x) and hours of chiller operation per day ( y) for a 3-ton residential gas air-conditioning system:

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x 72 78 80 86 88 92 4.8 y 7.2 9.5 14.5 15.7 17.9 Suppose that the system is actually a prototype model, and the manufacturer does not wish to produce this model unless the data strongly indicate that when maxi- mum outdoor temperature is 82F, the true average number of hours of chiller operation is less than 12. The appropriate hypotheses are then Ho: a (82) 12 versus Ha a + B(82) < 12 Use the statistic t a+b(82) - 12 Sa+682) which has a t distribution based on (n - 2) df when Ho is true, to test the hypotheses at significance level .01.