Finding a confidence interval.

[Hiche]

Homework Statement

A machine produces metal pieces that are cylindrical in shape. A sample of pieces is taken and the diameters are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, 1.03 centimeters. Find a 99% confidence interval for the mean diameter of pieces from this machine, assuming an approximately normal distribution.

Homework Equations

The Attempt at a Solution

From our data, we know N = 9. We find the sample mean X(bar) = 1.0056 and standard deviation s = ? (how exactly do we find this? Do we use the equation (1/n-1) * Ʃ (X_i - X(bar))²?. Moving on..

Since we have a normal population but UNKNOWN population variance, we muse use the t statistic: α = 0.01 and t_α/2 = 3.355 from the t-distribution table.

1.0056 ± (3.355) * s / √9 and then compute. Is this the way? Also, like I asked before, how do we find s exactly from our data?

 

[Ray Vickson]

Homework Statement

A machine produces metal pieces that are cylindrical in shape. A sample of pieces is taken and the diameters are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, 1.03 centimeters. Find a 99% confidence interval for the mean diameter of pieces from this machine, assuming an approximately normal distribution.

Homework Equations

The Attempt at a Solution

From our data, we know N = 9. We find the sample mean X(bar) = 1.0056 and standard deviation s = ? (how exactly do we find this? Do we use the equation (1/n-1) * Ʃ (X_i - X(bar))²?. Moving on..

Since we have a normal population but UNKNOWN population variance, we muse use the t statistic: α = 0.01 and t_α/2 = 3.355 from the t-distribution table.

1.0056 ± (3.355) * s / √9 and then compute. Is this the way? Also, like I asked before, how do we find s exactly from our data?

Just use the standard formulas that can be found in your textbook or in hundreds of sources on-line. The formula you wrote above is almost correct, but you wrote
$$s^2 = \left( \frac{1}{n}-1\right)\sum (x_i - \bar{x})^2$$
instead of the correct
$$s^2 = \frac{1}{n-1} \sum (x_i - \bar{x})^2 .$$ In other words, use (1/(n-1))!