Question

A study of the ability of individuals to walk in a straight line ("Can We Really Walk Straight?" American Journal of Physical Anthropology [1992]: \(19-27\) ) reported the following data on cadence (strides per second) for a sample of \(n=20\) randomly selected healthy men: \(\begin{array}{llllllllll}0.95 & 0.85 & 0.92 & 0.95 & 0.93 & 0.86 & 1.00 & 0.92 & 0.85 & 0.81\end{array}\) \(\begin{array}{llllllllll}0.78 & 0.93 & 0.93 & 1.05 & 0.93 & 1.06 & 1.06 & 0.96 & 0.81 & 0.96\end{array}\) Construct and interpret a \(99 \%\) confidence interval for the population mean cadence.

Short answer

The 99% confidence interval for the population mean cadence would be the result from step 4. These are the values within which we can be 99% confident that the true population mean lies.

Step-by-step solution

Calculation of Mean

Firstly, the mean (average) of these strides per seconds values needs to be calculated. The mean \(\mu\) is calculated as the sum of all values divided by the number of values.

Calculation of Standard Deviation

Next, the standard deviation is computed. The standard deviation \(s\) is found by calculating the square root of the variance. Variance is the average of the squared differences from the mean.

Determining the t-distribution value

Then, search for the t-value that corresponds to a 99% confidence level and 19 degrees of freedom (n-1) from the t-distribution table.

Calculation of Confidence Interval

Finally, the confidence interval is calculated. The formula for the confidence interval is \(\mu \pm (t * \frac{s}{\sqrt{n}})\), where \(\mu\) is mean, \(t\) is the t-value from step 3, \(s\) is the standard deviation, and \(n\) is the number of observations. This is going to give the lower and upper limits of the confidence interval.