A sleep researcher hypothesizes that college students who are deprived of sleep

Question

A sleep researcher hypothesizes that college students who are deprived of sleep will perform significantly lower on tests of cognitive ability than the general student body who likely slept around eight hours. One standardized test of cognitive ability, called the STCA, reveals that mean score for college students who slept around eight hours is µ = 4.5. Scores on the STCA range from 1-9 with high scores indicating better performance. The researcher brings 15 volunteer participants into the sleep lab one night and limits their sleep to four hours. The next morning he administers the STCA. Their scores are below.

2, 3, 3, 2, 5, 3, 3, 3, 6, 7, 2, 5, 4, 3, 4

Set your alpha level at = .05. Complete steps 3 and 4 of the hypothesis testing procedure. Then summarize the results of the hypothesis testing procedure by putting your results in journal form. Ignore the minus sign if your calculated z or t is negative. [Note, if your calculated z or t is not identical to one of the values below, but within plus or minus 0.2 of an answer below, assume it’s a rounding error and select the answer that is closest to your calculated value.]

Explanation / Answer

Null hypothesis:

H0: µ = 4.5

Alternative Hypothesis:

Ha: µ < 4.5

left tail t test

Alpha=0.05

Calculation of test statistic

sample mean=sum/total=55/15=3.67

stddev=1.496

t=samplemean-popmean/samplesd/sqrt(n)

=3.67-4.5/1.496(sqrt(15)

t=-2.15

Df=n-1=15-1=14

p=0.0248

p<0.05

Reject Null hypothesis.

Accept alternative hypothesis.

There is sufficient evidence at 5% level of signiifcance to conclude that college students who are deprived of sleep will perform significantly lower on tests of cognitive ability than the general student body who likely slept around eight hours.

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