statistics question

Question

The ability of lizards to recognize their predators can often mean life or death for lizards. By flicking their tongues, lizards can help determine if a predator is close by. Seventeen juvenile common lizards were exposed to the chemical cues of the viper snake. Then for each lizard, the number of tongue flicks per 20 minutes was recorded. The data are presented below. 

540, 472, 268, 472, 319, 200, 489, 353, 523, 421, 

302, 421, 200, 540, 251, 404, 438



a) Use this data to find a 90% confidence interval for the mean number of tongue flicks per 20 minutes for all juvenile common lizards when the chemical cues for a viper snake are present. (hint: since you will have to estimate the standard deviation using the sample data, you will have to use the t-distribution) 

Answer 1

For a 90% confidence interval, level of significance (alpha/2) is 0.05 on each side of the confidence interval.

The formula for the confidence interval is:

Xbar (mean) +/- t (0.05 alpha, n-1 = 17 - 1 = 16 degrees of freedom) * standard error

The mean is sum of data points / 17 = 6613/17 = 389

t (0.5 alpha, 16 DOF) = 1.746

The sample standard deviation = 114.8

standard error = sample standard deviation/square root (17) = 27.84

So the confidence interval is:

389 +/- 1.746 * 27.84

389 +/- 48.6

[340.4,437.6]