Question

A sample of 8 buttons is randomly selected and the following diameters are measured in inches. Give a point estimate for the population standard deviation. Round your answer to three decimal places. 1.83,1.85,1.79,1.73,1.69,1.74,1.76,1.70

Answer 1

Answer:

$\bar X= \frac{1.83+1.85+1.79+1.73+1.69+1.74+1.76+1.70}{8}= 1.76125$

Now we can estimate the population variance with the sample variance given by:

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

And replacing we got:

$s^2 = 0.0033839$

And the estimator for the population deviation $\sigma$ is given by :

$\hat \sigma = \sqrt{s^2}= \sqrt{0.0033839}= 0.058172$

Step-by-step explanation:

For this case we have the following data given:

1.83,1.85,1.79,1.73,1.69,1.74,1.76,1.70

First we need to calculate the mean with the following formula:

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

And replacing we got:

$\bar X= \frac{1.83+1.85+1.79+1.73+1.69+1.74+1.76+1.70}{8}= 1.76125$

Now we can estimate the population variance with the sample variance given by:

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

And replacing we got:

$s^2 = 0.0033839$

And the estimator for the population deviation $\sigma$ is given by :

$\hat \sigma = \sqrt{s^2}= \sqrt{0.0033839}= 0.058172$