A study of the ability of individuals to walk in a straight line reported the accompanying data on cadence (strides per second) for a sample of n = 20 randomly selected healthy men.
0.92 0.85 0.92 0.95 0.93 0.85 1.00 0.92 0.85 0.81 0.76 0.93 0.93 1.05 0.93 1.06 1.08 0.96 0.81 0.95
A normal probability plot gives substantial support to the assumption that the population distribution of cadence is approximately normal. A descriptive summary of the data from Minitab follows.
Variable N Mean Median TrMean StDev SEMean
cadence 20 0.9230 0.9300 0.9233 0.0848 0.0190
Variable Min Max Q1 Q3
cadence 0.7600 1.0800 0.8500 0.9550
(a) Calculate and interpret a 95% confidence interval for population mean cadence. (Round your answers to four decimal places.)
( ,) strides per second
Interpret this interval. Choose one from (1) ~ (3)
(1)With 95% confidence, the value of the true mean cadence of all such men falls below the confidence interval. (2)With 95% confidence, the value of the true mean cadence of all such men falls above the confidence interval. (3)With 95% confidence, the value of the true mean cadence of all such men falls inside the confidence interval.
(b) Calculate and interpret a 95% prediction interval for the cadence of a single individual randomly selected from this population. (Round your answers to four decimal places.)
( , ) strides per second
Interpret this interval. Choose one from (1) ~ (4)
(1)If this bound is calculated once, there is a 5% chance that these bounds will capture a future individual value of cadence for a healthy man.
(2)If this bound is calculated sample after sample, in the long run, 95% of these bounds will capture a future individual value of cadence for a healthy man.
(3)If this bound is calculated once, there is a 95% chance that these bounds will capture a future individual value of cadence for a healthy man.
(4)If this bound is calculated sample after sample, in the long run, 95% of these bounds will fail to capture a future individual value of cadence for a healthy man.
(c) Calculate an interval that includes at least 99% of the cadences in the population distribution using a confidence level of 95%. (Round your answers to four decimal places.)
( , )strides per second
Interpret this interval. Choose one from (1) ~ (4)
(1)We can be 99% confident that the interval includes at least 95% of the cadence values in the population.
(2)We can be 95% confident that the interval includes at least 99% of the cadence values in the population.
(3)We can be 1% confident that the interval includes at least 95% of the cadence values in the population.
(4)We can be 5% confident that the interval includes at least 99% of the cadence values in the population.