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Assignment C Secure https://www.webassign.net/webstudent/Assignment-Responses. a o 3 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. 0.95 0.85 0.92 0.95 0.93 0.86 1.00 0.92 0.85 0.81 0.76 0.93 0.93 1.04 0.93 1.06 1.09 0.96 0.81 0.97 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 cadence Variable cadence N Mean Median TrMean StDer SEMean 20 .92600.9300 0.9261 0.0852 0.0191 Min 0.7600 1.0900 0.8550 0.9650 23 (a) Calculate and interpret a 95% confidence interval for population mean cadence. (Round your answers to four decimal places.) (loss51 |v 'ose59 ) strides per second 0 9659 Interpret this 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 inside the confidence interval. o 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.) 11043 ) strides per second 0.7477 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 sample after sample, in the long run, 95% of these bonds will fail to 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 once, there is a 95% chance that these bounds will capture a future individual value of cadence for a healthy man. 0 (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.) 0.6180 X1.2340 xstrides per second Interpret this interval.

Explanation / Answer

The formula for estimation is:

= M ± t(sM)

where:

M = Mean

t = t statistic determined by confidence level
sM = standard error = (s2/n)

M = 0.926
t = 2.09
sM = (0.08522/20) = 0.02
So, the 95% confidence interval is,
= M ± t(sM)
= 0.926 ± 2.09*0.02
= 0.926 ± 0.0418

=> 0.926-0.0418 < mu < 0.926+0.0418

=> 0.8842 < mu < 0.9678

Therefore the 95% confidence interval is (0.8842 , 0.9678) strides per second.

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