A study of the ability of individuals to walk in a straight line reported the ac
ID: 3299067 • Letter: A
Question
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. 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. (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. With 95% confidence, the value of the true mean cadence of all such men falls inside the confidence interval. With 95% confidence, the value of the true mean cadence of all such men falls above the confidence interval. With 95% confidence, the value of the true mean cadence of all such men falls below 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. 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. 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. 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. 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. (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. We can be 5% confident that the interval includes at least 99% of the cadence values in the population. We can be 1% confident that the interval includes at least 95% of the cadence values in the population. We can be 99% confident that the interval includes at least 95% of the cadence values in the population. We can be 95% confident that the interval includes at least 99% of the cadence values in the population.Explanation / Answer
a. The 95% c.i for population mean cadence, mu is: xbar+-talpha/2, df=n-1 (s/sqrt n), where, xbar is sample mean, t is critical t value at alpha/2 (alpha=0.05, alpha/2=0.05/2=0.025) and n-1 degrees of freedom, n is sample size, s is sample standard deviation.
=0.9240+-2.0930(0.0796/sqrt 20)
=(0.8867,0.9613)
Corret interpretation for the c.i is that one can be 95% confident that the mean cadence of all such men falls inside the confidence interval. Therefore, option a is correct. Options b and c are discarded.
b.
The 95% p.i for the cadence of a single individual randomly selcted from the population,is: xbar+-talpha/2, df=n-1 s sqrt(1+1/n), where, xbar is sample mean, t is critical t value at alpha/2 (alpha=0.05, alpha/2=0.05/2=0.025) and n-1 degrees of freedom, n is sample size, s is sample standard deviation.
=0.9240+-2.0930*0.0796 sqrt (1+1/20)
=(0.7533,1.0947)
c. The tolerance interval which includes atleast 99% of the cadences in the population distribution using a confidence level of 95% is: xbar+-talpha/2,df=n-1s=0.9240+-3.1737(0.0796)=(0.6714, 1.1766)
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