Construct a 98% confidence interval for the population mean length of time?

Question

Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You collect data from a random sample of 12 patients. The period of effectiveness of the tranquilizer for each patient (in hours) is as follows:

2.6
2.3
2.5
2.6
2
2.3
2.3
2.9
2.3
2.8
2.7
2

Construct a 98% confidence interval for the population mean length of time. Enter your answer as an open-interval (i.e., parentheses) Round upper and lower bounds to two decimal places

Answer 1

compute the mean and standard deviation of the data set

98% CI = mean +/- margin of error

margin of error = t-critical * standard deviation/square root(sample size)

t-critical for 98% CI is sample size - 1 degrees of freedom (DOF). Look up t-score in t-table for sample size - 1 DOF and alpha = alpha/2 = 0.01.