Question

MY NOTES 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. PRACTICE ANOTHER 0.95 0.85 0.92 0.95 0.93 0.85 1.00 0.92 0.85 0.81 0.75 0.93 0.93 1.03 0.93 1.06 1.09 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 St Dev SEMean cadence 20 0.9235 0.9300 0.9239 0.0856 0.0191 Variable Min Max Q1 cadence 0.7500 1.0900 0.8500 0.9550 (a) Calculate and interpret a 95% confidence interval for population mean cadence. (Round your answers to four decimal places.) I. 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 below the confidence interval. With 95% confidence, the value of the true mean cadence of all such men falls above 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.)

Answer 1

a)

sample mean 'x̄=		0.9235
sample size    n=		20
std deviation s=		0.0856
std error ='sx=s/√n=0.0856/√20=		0.0191

for 95% CI; and 19 df, value of t=		2.0930		from excel: t.inv(0.975,19)
margin of error E=t*std error    =		0.0401
lower bound=sample mean-E =		0.8834
Upper bound=sample mean+E =		0.9636
from above 95% confidence interval for population mean =(0.8834 , 0.9636)

With 95% confidence, the value of the true mean cadence of all such men falls inside the confidence interval with /

b)

std errror of mean ='sx=s*√(1+1/n)=		0.088
for 95% CI; and 19 df, value of t=		2.093		from excel: t.inv(0.975,19)
margin of error E=t*std error    =		0.1836
lower bound=sample mean-E =		0.7399
Upper bound=sample mean+E=		1.1071
from above 95% prediction interval for population mean =(0.7399 ,1.1071)

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 If thin

c)

for sample size n=20& 99% tolerance level with 95% CI value of k=		3.6150
sample mean                  x̅=		0.924
standard deviation       σ=		0.086
margin of error              E =	k*std deviation	0.309
lower tolerance level     =	sample mean -E                                                =	0.6141
Higher tolerance level   =	sample mean +E                                                =	1.2329

interval =(0.6141 ,1.2329)