11. Research has suggested that losing even one night\'s sleep can have a signif

Question

11. Research has suggested that losing even one night's sleep can have a significant effect on performance of complex tasks, such as problem solving (Linde & Bergstroem, 1992). In a hypothetical study, a sample of n-1000 participants is given a problem-solving task after having a good night sleep. Then, researchers by means of phone calls and environmental distractions ensured that students did not get enough sleep the next night and tested them again. They documented a statistically significant Mp-1.5 (the number of correct responses, on average, decreased). The standard deviation for the differences was s-9. Can the researchers conclude that the loss of one night of sleep had medium to large effect on participants' problem-solving abilities (Cohen's d)? If not, why do you think researchers have founda statistically significant result? (Hint: pay attention to the sample size) (6 points) Yes,yor encomelad ect the loss of one nigist of sep Jors ha a medi sb e foss ot one ninlc 0.2 isa 12. State the assumptions of an independent-measures t-test (3 points)

Explanation / Answer

When effect size is small then the test is not practically significance even thought it is statistically significant.

Also note than if the difference between hypothetical value and estimated value is small and sample size is very large then the absolute test statistic value is large and so we reject null hypothesis even there is small difference.

So that we need to used Cohen's d for checking the effect of the test.

12) Assumptions of independent - measure t test.

1) Sample comes from normal distribution.

2) If sample is not comes from normal distribution then the sample size is at least 30

3) Both the samples are independent

For pooled t test we assume that the standard deviations of both the population are same.

For unpooled t test we assume that the standard deviations of both the population are not same.

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