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06.05.2020 •
Mathematics
Suppose we want to assess the effect of music on concentration. We measure "concentration" by recording the time it takes a person to complete a simple word puzzle. Each person does a puzzle with and without music. A coin flip determines the order of the treatments. Our subjects are a sample of 18 volunteers from a statistics class. We test the hypotheses (at the 5% level): H 0: μ = 0 H a: μ > 0 where μ is the mean of the difference in times ("no music" minus "music"). The sample mean is 4 seconds with a standard deviation of 9 seconds. The sample is not random, but treatments are randomly ordered. In addition, the distribution of times is not strongly skewed, so we decide to use the t-test despite the small sample size. The t-test statistic is approximately 1.89 with a P-value of approximately 0.038. What can we conclude?
a. Music is not associated with statistically significant improvements in concentration as measured by time to complete a simple word puzzle.
b. Completion times only increased 4 seconds on average. For college students, music produces statistically significant improvements in concentration as measured by time to complete a simple word puzzle.
c. College students listening to music performed significantly faster on word puzzles than students who were not listening to music.
d. For college students, music is associated with statistically significant improvements in concentration as measured by time to complete a simple word puzzle.
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Ответ:
d. For college students, music is associated with statistically significant improvements in concentration as measured by time to complete a simple word puzzle.
Step-by-step explanation:
Hello!
The variable of interest is
Xd: Difference between the time that takes a person to complete a simple word puzzle without music and with music.
The parameter of interest is the mean difference between the two times.
The claim is that music increases the concentration and thus decreases the time it takes a person to resolve the word puzzle. If so then the mean difference between the two times should be positive, μ > 0.
H₀: μ = 0
H₁: μ > 0
α: 0.05
p-value= 0.038
The decision rule using the p-value approach is:
If the p-value ≤ α, then you reject the null hypothesis.
If the p-value > α, then you don't reject the null hypothesis.
The p-value is less than the level of significance, so the decision is to reject the null hypothesis, then the population mean of the difference between the time it takes a person resolve a puzzle without music and the time it takes a person resolve the puzzle with music is greater than zero. You can conclude that music increases concentration.
I hope this helps!
Ответ:
Step-by-step explanation:
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