Question

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?

Answer 1

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

Explanation:

`\\`Summing up the samples given , we have 331.6

`\\`Therefore , sample mean = 331.6/36

`\\`≈9.2

`\\`The standard deviation is ≈ 0.38

`\\`Since n > 30 , then we use Z- statistics

`\\`Let
`H_(0)` : Average EER = 9

`\\`
`H_(1)` : Average ≠ 9

`\\`using the z - formula

`\\`z =
`(x - u)/(s/√(n) )`

`\\`=
`(9.2-9)/(0.38/√(36) )`

`\\`= 3. 15

`\\`Checking the z- value at 0.05 , we have 1.64

`\\`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