Question

In a sample of 10 cabinets, the average height was found to be 37.3in. with a standard deviation of 3.



Give a point estimate for the population variance of the height of the cabinets. Round your answer to two decimal places, if necessary.

Answer 1

Answer:

$\sigma^2 = 3^2 \frac{10-1}{10}= 8.10$

Step-by-step explanation:

For this case we have a sample of n =10 and we have the following statistics:

$\bar X = 37.3 , s= 3$

And we want to estimate the population variance. We need to remember that the population variance is given by this formula:

$\sigma^2 =\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n}$

And the sample variance is given by:

$s^2 =\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}$

And we can find a formula for the population variance in terms of the sample deviation like this:

$\sigma^2 = s^2 \frac{n-1}{n}$

And replacing we got:

$\sigma^2 = 3^2 \frac{10-1}{10}= 8.10$