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. 0.94 0.85 0.92 0.95 0.93 0.86 1.00 0.92 0.85 0.81 0.78 0.93 0.93 1.03 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 St Dev SEMean cadence 20 0.9245 0.9300 0.9239 0.0810 0.0181 Variable Min Max Q1 03 cadence 0.7800 1.0800 0.8550 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. O 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. O 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.) strides per second Interpret this interval. 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 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. 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. We can be 99% confident that the interval includes at least 95% of the cadence values in the population. 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 95% confident that the interval includes at least 99% of the cadence values in the population.

Answer 1

Mean Median To Mean stoev sEMean ago 0.9905 0.9300 10.9339 0.osloo 081 Sol The available information is as shown below. N Cadence df-n-1 20-1 - 19. a) b). Calculate the 95%. Prediction interval to the cadence Variable At 95% twritical = 2.093. 0.9245 + 2.093 :0810 = 0.9245 + 0.0379 (951. (I = (0.8866, 0.9624) Hence, the pezuired conbidence interval is (08866<u of a single individual randomly selected from the Population. 95%. C. II It critical (5) Sith 95%CI= x + taticall) 2 0.9624 0.9245 +2.093 (0.0810) 0.9245 + 0.1737 959 (I = (0.7508, 1.0982) The reuered confidence interval is 0.7508 <l<1.0982.

an calculate interval that includes at least 99% to the codences in the population distribution using confidence level of 95% From the above Tolerance Factors for Normal distribution critical values at the n=20 with 99% confidence level is 3.615 Tolerance Interval = x I Tolerance Coritical (5) = 0.9245 +3.615 (0.0810) = 0.9245 +0.292815 Tolerance Interval= (0.631685, 1.217315) The greqished answer is, (0.6316.1.2173)

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