Energy efficiency rating - Math Problem Example

SBIT Statistics work July 2005 Question a. In the question regarding the relationship between an air conditioning unit's energy efficiency rating (EER) and its cost given the 7 data pairs (EER, Cost); the least square straight line is: y = -167.0 + 56.0xwhere; 1 = 7 (25292) - (67.5) (2610) = 56 7 (653.11) - (67.5)2and 0 = 2610 - 56 (67.5) = - 167b. The researcher can now conclude that there is a negative linear correlation between EER and cost. One can now predict whether the cost of an air conditioning unit is reasonable, from a given EER.

Thus, if it is considered that the best EER is, for example, 11.0, the least square line predicts that its estimated cost should be 449. In the event that it goes beyond that, the unit may be considered too expensive. Furthermore, if manufacturers discover that customers are not willing to pay for air conditioning units beyond 449, then they may be compelled to produce units that do not go beyond an 11.0 EER to limit costs. c. Based on the correlation coefficient, 0.913, 83.4% of the variation in cost is explained by the EER, while 16.

6% is explained by other causes.r = 25292 - (67.5) (2610) 7 .. [(653.11) - (4556.25 /7)] [(96100.0) - (6812100 / 7)] = 0.913d. y = 0 + 1xy = a + bx where: a= -167. (a = 63. ) = b0 = y interceptb= 56.0 (b = 6.9 ) = b1 = slopedegrees of freedom = 5r = 0.913 (p = 0.004) Question # 3a. Based on the comparison of nurses' salaries between private and government-owned hospitals (GOH), the mean, standard deviation, and variance for the two groups are as follows:GroupPrivateGOH Mean20764.5020350.83SD1573.931623.09Variance2477255.

6452634421.148In comparing the means for both groups, using a 1% significance level, the two-tailed P value, at a 99% confidence interval, equals 0.6543. Thus, there is a 65.43% probability that the observed difference between the salaries between private and GOH nurses are actually more extreme than their true differences. At a 1% level of significance, this implies that there is not enough statistical evidence to indicate that the salaries in private hospitals are greater than those in GOH. b.

Comparing the means between the previous and current salaries, the previous salaries' mean is higher than the current salaries. At a 99% confidence interval, the two-tailed p-value equal to 0.4699 indicates that there is no reason to conclude that the means have a significant difference. In addition, the lower confidence limit of -3739.9893 indicates a large decrease in the lower limit coupled with a large increase in the upper confidence limit of 2033.3093. Thus, there is no conclusive evidence that the previous salaries are significantly lower than current ones.

GroupGOH currentGOH previousMean20350.8321204.17SD1623.092213.81Variance2634421.4900954.716