As the prices of heating oil and natural gas increase, consumers become more careful about heating their homes. Researchers want to know how warm home owners keep their houses in January and how the results from Wisconsin and Tennessee compare. The researchers randomly call 23 Wisconsin households between 7 P.M. and 9 P.M. on January 15 and ask the respondent how warm the house is according to the thermostat. The researchers then call 19 households in Tennessee the same night and ask the same question. The results follow.
Wisconsin
71 71 65 68
70 61 67 69
75 68 71 73
74 68 67 69
69 72 67 72
70 73 72
Tennessee
73 75 74 71
74 73 74 70
72 71 69 72
74 73 70 72
69 70 67
For α=.01, is the average temperature of a house in Tennessee significantly higher than that of a house in Wisconsin on the evening of January 15? Assume the population variances are equal and the house temperatures are normally distributed in each population.