At the Olympic level of competition, even the smallest factors can make the difference between winning and losing. For example, it’s been shown that Olympic marksmen shoot much better if they fire between heartbeats, rather than squeezing the trigger during a heartbeat. The small vibration caused by a heartbeat seems to be sufficient to affect the marksman’s aim. The following hypothetical data demonstrate this phenomenon – assume the population of difference scores is normally distributed. A random sample of n = 6 Olympic marksmen fires a series of rounds while a researcher records heartbeats. For each marksman, a score is recorded for shots fired during heartbeats and for shots fired between heartbeats. Do the data indicate a difference? Test with α = 0.05. Also find an 80% confidence interval for μd. a. State the random variable and the parameter in words. b.State the null and alternative hypotheses and the level of significance. c. State and check the assumptions for a hypothesis test. During Heartbeats Between Heartbeats 93 95 90 94 95 96 92 91 95 94 91 95 91 93 89 90 95 95 96 94 92 92 93 97 90 93 95 92 91 94 96 98 94 94 89 93 93 94 93 92 92 90 91 95 95 95 96 98 90 91 94 93 92 90 93 98 91 95 96 93 96 95 93 95 94 95 89 93 91 94 96 95 94 92 95 94 89 92 90 94 90 93 91 91 92 93 92 94 93 94 94 95 93 95 94 93 95 95 92 91 90 92 91 93 95 93 96 95 97 94 90 93 96 93 93 94 96 93 90 91 92 95 90 94 90 93 91 91 92 93

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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At the Olympic level of competition, even the smallest factors can make the difference between winning and losing. For example, it’s been shown that Olympic marksmen shoot much better if they fire between heartbeats, rather than squeezing the trigger during a heartbeat. The small vibration caused by a heartbeat seems to be sufficient to affect the marksman’s aim. The following hypothetical data demonstrate this phenomenon – assume the population of difference scores is normally distributed. A random sample of n = 6 Olympic marksmen fires a series of rounds while a researcher records heartbeats. For each marksman, a score is recorded for shots fired during heartbeats and for shots fired between heartbeats. Do the data indicate a difference? Test with α = 0.05. Also find an 80% confidence interval for μ_d.

a. State the random variable and the parameter in words.

b.State the null and alternative hypotheses and the level of significance.

c. State and check the assumptions for a hypothesis test.

During Heartbeats	Between Heartbeats
93	95
90	94
95	96
92	91
95	94
91	95
91	93
89	90
95	95
96	94
92	92
93	97
90	93
95	92
91	94
96	98
94	94
89	93
93	94
93	92
92	90
91	95
95	95
96	98
90	91
94	93
92	90
93	98
91	95
96	93
96	95
93	95
94	95
89	93
91	94
96	95
94	92
95	94
89	92
90	94
90	93
91	91
92	93
92	94
93	94
94	95
93	95
94	93
95	95
92	91
90	92
91	93
95	93
96	95
97	94
90	93
96	93
93	94
96	93
90	91
92	95
90	94
90	93
91	91
92	93

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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