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A consumers’ advocate group would like to evaluate the average energy efficiency (EER) of window mounted, large-capacity air conditioning units. A random sample of 36 units is selected and tested for a fixed period of time. Their EER records are as follows: 8.9 9.1 9.2 9.1 8.4 9.5 9.0 9.6 9.3 9.3 8.9 9.7 8.7 9.4 8.5 8.9 8.4 9.5 9.39.3 8.8 9.4 8.9 9.3 9.0 9.2 9.1 9.8 9.6 9.3 9.2 9.1 9.6 9.8 9.5 10.0Using the 0.05 level of significance, is there evi- dence that the average EER is different from 9.0?

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Answer: Yes , there is evidence that the average EER is different from 9.0

Step-by-step explanation:

[tex]\\[/tex]Summing up the samples given , we have 331.6

[tex]\\[/tex]Therefore , sample mean = 331.6/36

[tex]\\[/tex]≈9.2

[tex]\\[/tex]The standard deviation is ≈ 0.38

[tex]\\[/tex]Since n > 30 , then we use  Z- statistics

[tex]\\[/tex]Let [tex]H_{0}[/tex] : Average EER = 9

[tex]\\[/tex] [tex]H_{1}[/tex] : Average ≠ 9

[tex]\\[/tex]using the z - formula

[tex]\\[/tex]z = [tex]\frac{x - u}{s/\sqrt{n} }[/tex]

[tex]\\[/tex]= [tex]\frac{9.2-9}{0.38/\sqrt{36} }[/tex]

[tex]\\[/tex]= 3. 15

[tex]\\[/tex]Checking the z- value at 0.05 , we have 1.64

[tex]\\[/tex]Conclusion: since the z- calculate value is greater than the z-tab , then we reject the null hypothesis and conclude that there the average EER is different from 9

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