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

Answer:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

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:

$Bias = 38.91 -40 = -1.09$

Step-by-step 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:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

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:

$Bias = 38.91 -40 = -1.09$