A researcher wanted to see if live reggae music improved students\' math test sc
ID: 3133600 • Letter: A
Question
A researcher wanted to see if live reggae music improved students' math test scores^1 He selected a sample of 61 students from his university and gave them a math test. The students then studied for two and a half hours while an acoustic reggae band played quietly. The students then took another math test of the same difficulty. The researcher's variable was the change in test score for each student - a positive change meant the student did better after listening to reggae, while a negative change meant a student did worse. He found that the changes had an approximately normal distribution with mean 6.5 and standard deviation 12. Assuming the sample is random, test the hypothesis that the population average is positive. Does the study provide convincing evidence that live reggae music improves students' math test scores? Explain why or why not.Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: ud <= 0
Ha: ud > 0
As we can see, this is a right tailed test.
Getting the test statistic, as
Xd = sample mean = 6.5
uo = hypothesized mean = 0
n = sample size = 61
s = standard deviation = 12
Thus, z = (Xd - uo) * sqrt(n) / s = 4.230551908
Also, the p value is
p = 1.16559E-05
As P is very small, we REJECT THE NULL HYPOTHESIS.
Thus, there is significant eivdence that the population mean change in scores is positive. [CONCLUSION]
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b)
YES, there is significant evidence that the population mean change in scores is positive, as the P value is very small.
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