Question

Determine whether the given value is a statistic or a parameter.A homeowner measured the voltage supplied to his home on 42 random days, and the average (mean) value is 127.1 volts.A) The given value is a statistic for the year because the data collected represented a population.

B) The given value is a parameter for the year because the data collected represent a sample.
C) The given value is a parameter for the year because the data collected represent a population.
D) The given value is a statistic for the year because the data collected represent a sample.

Answer 1

`\bar X = (\sum_(i=1)^(42) X_i)/(n)`

And for this case the sample mean is

`\bar X = 127.1`

And this value is calculated from a sample so then can't represent a population parameter. Then the value 127.1 represent a statistic called the sample mean unbiased for the true population mean since
`E(\bar X) =\mu`, and the best option would be:

D) The given value is a statistic for the year because the data collected represent a sample.

Explanation:

For this case we know that a homeowner take a random sample of 42 voltage values ina year and he calculate the sample mean with this formula:

`\bar X = (\sum_(i=1)^(42) X_i)/(n)`

And for this case the sample mean is

`\bar X = 127.1`

And this value is calculated from a sample so then can't represent a population parameter. Then the value 127.1 represent a statistic called the sample mean unbiased for the true population mean since
`E(\bar X) =\mu`, and the best option would be:

D) The given value is a statistic for the year because the data collected represent a sample.