As the prices of heating oil and natural gases increase, consumers become more c

Question

As the prices of heating oil and natural gases increase, consumers become more careful about heating their homes. Researchers want to know how warm homeowners keep their houses in January and how the results between Wisconsin and Tennesse compare. The researchers randomly call 23 Wisconsin households between 7pm and 9pm. On January 15 and asked the respondent how warm the house is according to the thermostat. The researchers called 19 households in Tennessee the same night and ask the same question. The results are as follows:
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 a=0.01 is the average temperature of a house in Tennessee is significantly warmer than a house in Wisconsin on the evening of January 15? Assume that the population variances are equal and that the house temperatures are normally distributed in each population.

Explanation / Answer

Wisconsin µ1
Sample mean 69.65217
Sample standard deviation 3.156648

Tennessee µ2
Sample mean 71.73684
Sample standard deviation 2.156182

(statistics were computed using Excel spreadsheet).

Ho:µ1 =µ2 Ha: µ1 < µ2 T statistic= 69.65217-71.73684/sqrt[(2.156182)^2/19 + (3.156648)^2/23] T statistic= -2.08467/0.82336= -2.532 Look up in T table with degrees of freedom 18 (lesser of 23-1 and 19-1) .01 Very close call, but do not reject null hypothesis at .01 level. There is not significant evidence to support the contention that Tennessee has a higher mean temperature than Wisconsin.
Very close call, but do not reject null hypothesis at .01 level. There is not significant evidence to support the contention that Tennessee has a higher mean temperature than Wisconsin.

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