Question

A sample of 8 golf balls is randomly selected and the following weights are measured in grams. Give a point estimate for the population variance. Round your answer to three decimal places. 45.15,45.12,45.19,45.08,45.21,45.17,45.14,45.24

Answer 1

`\bar X = 45.1625`

And the sample variance is given by:

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

And replacing we got:

`s^2= 0.00262\approx 0.003`

And this one is the best estimator for the population variance
`\sigma^2`

Explanation:

For this case we have the following data:

45.15,45.12,45.19,45.08,45.21,45.17,45.14,45.24

The first step would be calculate the sample mean given by:

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

And replacing we got:

`\bar X = 45.1625`

And the sample variance is given by:

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

And replacing we got:

`s^2= 0.00262\approx 0.003`

And this one is the best estimator for the population variance
`\sigma^2`