A sleep researcher is assessing the impact of melatonin supplements on time to fall asleep for individuals with insomnia. She recruited 30 participants with insomnia and assigned 14 of them to take melatonin before sleeping. The researcher then recorded time to fall asleep (in minutes) for each participant. The researcher's hypothesis was that participants in the melatonin group would fall asleep faster than participants in the control group. The data collected are displayed below together with some descriptive statistics. Melatonin- 72, 59, 76, 64, 40, 51, 39, 69, 69, 78, 66, 100, 43, 45 M = 62.21 SD = 17.33 Control- 52, 80, 113, 111, 103, 96, 64, 56, 112, 102, 100, 102, 101, 58, 117, 101 M = 91.75 SD = 22.16 a) Does the researcher have enough evidence to reject the null hypothesis at an alpha level of .01? Follow the steps involved in hypothesis testing and make a decision regarding the null hypothesis based on the comparison between the critical value and the test statistic. b) Compute Cohen's d as an effect size for the difference between melatonin and control groups and interpret the obtained value. For the interpretation, it is not sufficient to state whether this is large, medium, or small effect. c) The standard deviations in the two groups are different. Which assumption of the hypothesis test applied to this example might therefore be violated?
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A sleep researcher is assessing the impact of melatonin supplements on time to fall asleep for individuals with insomnia. She recruited 30 participants with insomnia and assigned 14 of them to take melatonin before sleeping. The researcher then recorded time to fall asleep (in minutes) for each participant. The researcher's hypothesis was that participants in the melatonin group would fall asleep faster than participants in the control group. The data collected are displayed below together with some
Melatonin- 72, 59, 76, 64, 40, 51, 39, 69, 69, 78, 66, 100, 43, 45
M = 62.21
SD = 17.33
Control- 52, 80, 113, 111, 103, 96, 64, 56, 112, 102, 100, 102, 101, 58, 117, 101
M = 91.75
SD = 22.16
a) Does the researcher have enough evidence to reject the null hypothesis at an alpha level of .01? Follow the steps involved in hypothesis testing and make a decision regarding the null hypothesis based on the comparison between the critical value and the test statistic.
b) Compute Cohen's d as an effect size for the difference between melatonin and control groups and interpret the obtained value. For the interpretation, it is not sufficient to state whether this is large, medium, or small effect.
c) The standard deviations in the two groups are different. Which assumption of the hypothesis test applied to this example might therefore be violated?
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