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.
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
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 |
a)conclussion
b)Interpretation:
c)Statistical Interpretation:
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