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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 mean and standard deviation of the reaction times (in seconds) for these subjects were 1.82 seconds and 0.28 seconds, respectively. Previous psychological studies have shown 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 adult males is longer than that of non-sleep-deprived adult males?

A. H0: μ = 1.82; Ha: μ < 1.82
B. H0: μ = 1.70; Ha: μ < 1.70
C. H0: μ = 1.82; Ha: μ > 1.82
D. H0: μ = 1.70; Ha: μ > 1.70
E. None of the above

Answer :

Answer:

D. [tex]H_{0}[/tex] : μ = 1.70, [tex]H_{a}[/tex] : μ > 1.70

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to test a hypothesis

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

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Rewritten by : Jeany

Final answer:

The correct hypotheses to test whether the mean reaction time for sleep-deprived adult males is longer than for non-sleep-deprived males is D. Null hypothesis (H0): μ = 1.70 seconds; Alternative hypothesis (Ha): μ > 1.70 seconds.

Explanation:

The student is asking about setting up hypotheses for a hypothesis test to determine if the mean reaction time for sleep-deprived adult males is longer than that for non-sleep-deprived adult males. The correct set of hypotheses for this situation would compare the known population mean (μ) for non-sleep-deprived males (1.70 seconds) with the mean from the sample of sleep-deprived males. This leads us to:

Null hypothesis (H0): μ = 1.70 (The mean reaction time for sleep-deprived adult males is equal to that of non-sleep-deprived adult males.)

Alternative hypothesis (Ha): μ > 1.70 (The mean reaction time for sleep-deprived adult males is greater than that of non-sleep-deprived adult males.)

Thus, the correct answer to the student's question is D. H0: μ = 1.70; Ha: μ > 1.70.

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