What is the value of the the test statistic? Question follows \"New York is know

Question

What is the value of the the test statistic? Question follows "New York is known as the city that never sleeps". A random, independent sample of 25 New Yorkers were asked how much sleep they get per night. Statistical summaries of this data are shown below. Does this data provide strong evidence that New Yorkers sleep less than 8 hours a night on average? You may presume that in this population sleep lengths follow a normal distribution. Use a 1% level of significance. Fully show your working, and draw any relevant diagrams. Sample Results: Number = 25 Mean sleep length = 7.73 hours Standard deviation of sleep length = 0.77 hours Minimum 6.17 hours Maximum 9.78 hours"

Explanation / Answer

Ans:

sample size=25

sample mean=7.73

sample standard deviation=0.77

Standard error of the mean=0.77/sqrt(25)=0.154

Test statistic:

t=(7.73-8)/0.154=-1.753

df=25-1=24

p-value=P(t<-1.753)=tdist(1.753,24,1)=0.0462

As,p-value>0.01,we fail to reject null hypothesis.

There is not sufficient evidence to conclude that New Yorkers sleep less than 8 hrs a night on average.

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