The recommended number of hours of sleep per night is 8 hour

The recommended number of hours of sleep per night is 8 hours, but everybody \"knows\" that the average college student sleeps less than 7 hours. The number of hours slept last night by 10 randomly selected college students is listed below. Complete the following hypothesis test: H_o: ? = 7, H_a: ? < 7, ? = 0.05.

7.4    5.7   7.5    6.4    7.1    6.8    5.7    6    7.2    7

(a) Find t. (Give your answer correct to two decimal places

(ii) Find the p-value. (Give your answer correct to four decimal places.)

(b) State the appropriate conclusion.

Solution

(a) Find t. (Give your answer correct to two decimal places

sample mean=6.68

sample standard deviation =0.68443

t=(xbar-mu)/(s/vn)

=(6.68-7)/(0.68443/sqrt(10))

=-1.48

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(ii) Find the p-value. (Give your answer correct to four decimal places.)

It is a left-tailed test.

The degree of freedom =n-1=10-1=9

The p-value= P(t with df=9<-1.48)=0.0865 (from student t table)

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(b) State the appropriate conclusion.

Since the p-value is larger than 0.05, we do not reject the null hypothesis.

So we can not conclude that popluation mean is less than 7