Question 974224: 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: Ho: μ = 7, Ha: μ < 7, α = 0.05.
8 6.9 6.1 6.6 7.5 8 7.6 7.3 7.8 5.7
(a) Find t. (Give your answer correct to two decimal places.)
(ii) Find the p-value. (Give your answer correct to four decimal places.)
Found 2 solutions by Boreal, stanbon: Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! Ho: mu >=7
Ha: mu<7 The hypotheses must encompass the whole density function
a=0.05 1 tail test
Test statistic, t df=9
Critical value t (df=9) < -1.833 ;; (xbar-mu)/s/sqrt(9);; 3 (xbar-mu)/s
t=+0.5916 The mean is >7 (7.15), so the null hypothesis cannot be rejected a priori, since the data themselves show a mean greater than that which was postulated to be the maximum value.
p=0.7157, but this is a calculated value, and again the fact that the mean is not in the range of Ha makes rejecting Ho impossible with this sample.
Note: if it were two-tailed, it still wouldn't be rejected.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! 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.
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Complete the following hypothesis test using α = 0.05 :
Ho: μ = 7
Ha: μ < 7
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DATA:
8 6.9 6.1 6.6 7.5 8 7.6 7.3 7.8 5.7
x-bar = 7.15
s = 0.8
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(a) Find t. (Give your answer correct to two decimal places.)
t(7.15) = (7.15-7)/0.8 = 0.15/0.8 = 0.19
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(ii) Find the p-value. (Give your answer correct to four decimal places.)
p-value = P(t < 0.19 when df = 9) = tcdf(-100,0.19,9) = 0.58
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Conclusion:: Since the p-value is greater than alpha, fail to
reject Ho.
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Cheers,
Stan H.
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