A psychologist is studying the effects of lack of sleep on the performance of various perceptual-motor tasks. After a given period of sleep deprivation, a measurement of reaction time to an auditory stimulus was taken for each of 36 adult male subjects. The reaction times (in seconds) are summarized as follows:

\[ \bar{x} = 1.82, \ s = 0.22 \]

Previous psychological studies show that the true mean reaction time for non-sleep-deprived male subjects is 1.70 seconds. Does the sample evidence indicate that the mean reaction time for sleep-deprived male subjects is longer than that of non-sleep-deprived male subjects?

\[ \alpha = 0.05 \]

The alternative hypothesis for the above problem is:

A. $ \mu \neq 1.70 $

B. $ \mu > 1.70 $

C. $ \mu = 1.70 $

D. $ \mu < 1.70 $

Question

04-07-2024
Mathematics

High School

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A psychologist is studying the effects of lack of sleep on the performance of various perceptual-motor tasks. After a given period of sleep deprivation, a measurement of reaction time to an auditory stimulus was taken for each of 36 adult male subjects. The reaction times (in seconds) are summarized as follows:

\[ \bar{x} = 1.82, \ s = 0.22 \]

Previous psychological studies show that the true mean reaction time for non-sleep-deprived male subjects is 1.70 seconds. Does the sample evidence indicate that the mean reaction time for sleep-deprived male subjects is longer than that of non-sleep-deprived male subjects?

\[ \alpha = 0.05 \]

The alternative hypothesis for the above problem is:

A. $ \mu \neq 1.70 $

B. $ \mu > 1.70 $

C. $ \mu = 1.70 $

D. $ \mu < 1.70 $

Answer :

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MariaRobell MariaRobell · Answer 1 · 2023-08-05T02:34:14-04:00

Final answer:

The correct alternative hypothesis for the study on the effects of lack of sleep on perceptual-motor tasks reaction times is that the mean reaction time for sleep-deprived subjects (μ) is greater than that of non-sleep-deprived subjects (1.70 seconds).

Explanation:

The student is investigating whether sleep deprivation increases reaction time to an auditory stimulus by comparing the mean reaction time of a sample of sleep-deprived adult males to the known mean reaction time of non-sleep-deprived males. The null hypothesis in this study would typically assume that there is no difference between the mean reaction time of the sleep-deprived and non-sleep-deprived male subjects.

The alternative hypothesis, which represents what we are trying to find evidence for, should reflect the research question, which in this case is whether sleep deprivation leads to longer reaction times. Therefore, the correct alternative hypothesis to test would be μ > 1.70, which states that the mean reaction time for sleep-deprived male subjects is greater than 1.70 seconds, the mean reaction time for non-sleep-deprived male subjects.