Question

Consider a normal population with the mean of 40 and standard deviation of 10. A random sample of was selected: 39.2, 45.7, 27.4, 25.9, 25.1, 46.3, 42.9, 49.0, 40.6, 47.0. What is the bias of this the estimated mean for this sample

Answer 1

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

And replacing we got:

`\bar X= 38.91`

And we can find the bias with this formula:

`Bias= \bar X -\mu`

And replacing we got:

`Bias = 38.91 -40 = -1.09`

Explanation:

For this problem we know that the random variable of interest follows this distribution:

`X \sim N(\mu =40, \sigma= 10)`

And we have the following random sample given:

39.2, 45.7, 27.4, 25.9, 25.1, 46.3, 42.9, 49.0, 40.6, 47.0

And we can calculate the sample mean with the following formula:

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

And replacing we got:

`\bar X= 38.91`

And we can find the bias with this formula:

`Bias= \bar X -\mu`

And replacing we got:

`Bias = 38.91 -40 = -1.09`