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The recommended number of hours of sleep per night is 8 hours, but everybody "knows" that...

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.

6 5.5 6.9 7.6 6.3 7.4 5.3 6.1 5.5 7.6

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

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

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Answer #1

From sample data,

\bar{x} = 6.42

S = 0.8954

a)

Test statistics

t = \bar{x} - \mu / S / sqrt(n)

= 6.42 - 7 / 0.8954 / sqrt(10)

= -2.05

b)

From T table,

With test statistics t = -2.05 and df = 9,

p-value = 0.0353

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