Question

As the prices of heating oil and natural gas 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 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 Tennessee

71 71 65 68 73 75 74 71
70 61 67 69 74 73 74 70
75 68 71 73 72 71 69 72
74 68 67 69 74 73 70 72
69 72 67 72   69 70 67
70 73 72

For alpha= 0.01, 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.

Answer 1

Answer:

Given Data

sample 1 :

Mean = 69.65,

= 3.16

Sample 2 :

Mean   = 71.74

= 2.16

The level of significance is

against

under test statistic

So we do not reject our null hypothesis.

i.e . Hence we conclude that there is not sufficient evidence to conclude that is the average temperature of a house in Tennessee significantly warmer that a house in wisconsin on the evening of January 15.

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