At the Olympic level of competition, even the smallest factors can make the difference between winning and losing. For example,
Pelton (1983) has 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. Olympic marksmen fire 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.
Answer the following questions.
1. Focus on the Descriptive Statistics output. Compare the means for the two conditions. Remember that the marksmen were measured twice, when they shot during heartbeats and when they shot between heartbeats. At which time, during or between, did they score more points?
2. Focus on the Paired Samples T-Test output. a. What is the value for t? b. What is p? p is the exact alpha that corresponds to the value for t. c. Should the researcher reject or retain the null hypothesis? d. Note that a paired-samples t-test is the same thing as a repeated- measures t-test.
3. If there’s a difference in shots taken during and between heartbeats, you should expect to see a significant difference between the two conditions. According to the findings reported in the output above, was there a significant difference between the scores for the marksmen during and between heartbeats?
Answer the following questions.
1. Focus on the Descriptive Statistics output. Compare the means for the two conditions. Remember that the marksmen were measured twice, when they shot during heartbeats and when they shot between heartbeats. At which time, during or between, did they score more points?
2. Focus on the Paired Samples T-Test output. a. What is the value for t? b. What is p? p is the exact alpha that corresponds to the value for t. c. Should the researcher reject or retain the null hypothesis? d. Note that a paired-samples t-test is the same thing as a repeated- measures t-test.
3. If there’s a difference in shots taken during and between heartbeats, you should expect to see a significant difference between the two conditions. According to the findings reported in the output above, was there a significant difference between the scores for the marksmen during and between heartbeats?
1 answer:
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Answer:
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
Since the distribution for X is normal then the we know that the distribution for the sample mean is given by:
And the standard error is given by:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
Since the distribution for X is normal then the we know that the distribution for the sample mean is given by:
And the standard error is given by: