Question

Suppose that the random variable X represents the amount of electrical energy used (in kwH) in a month for residents in Virginia. The historical amount of electrical energy used in a month for residents is 102 kwH. The following data (in kwH per month) were recorded from a random sample of 8 residents: 111 113 145 105 90 100 150 88(a) Calculate the mean and sample variance of X. (b) What is t statistic with this problem?

Answer 1

a)
`\bar X = (\sum_(i=1)^n X_i)/(n)`

`\bar X = 112.75`

`s^2 = (\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)`

`s^2 = 540.5`

b)
`t = (\bar X -\mu)/((s)/(√(n)))`

And if we replace we got:

`t = (112.75-112)/((23.249)/(√(8)))= 0.0912`

Explanation:

Part a

For this case we have the following data: 111 113 145 105 90 100 150 88

We can calculate the mean with the following formula:

`\bar X = (\sum_(i=1)^n X_i)/(n)`

And replacing we got:

`\bar X = 112.75`

And the sample variance can be calculated with this formula:

`s^2 = (\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)`

And replacing we got:

`s^2 = 540.5`

Part b

For this case we want to check is the true mean is equal to 102 or no, the t statistic is given by:

`t = (\bar X -\mu)/((s)/(√(n)))`

And if we replace we got:

`t = (112.75-112)/((23.249)/(√(8)))= 0.0912`