A researcher is concerned that graduate students get less than the recommended 8 hours of sleep a night. She selects a random sample of 45 students at a local university and asks them how much sleep they get on a typical night.

H0 : μ = 8

H1 : μ < 8

Test statistic = - 7.51

conclude that there is statistical significance that student at the school get less than 8 hours of sleep on average.

Step-by-step explanation:

The hypothesis :

H0 : μ = 8

H1 : μ < 8

The test statistic :

(xbar - μ) ÷ (s/√(n))

Sample data :

1.75, 2, 2.25, 2.25, 2.5, 3, 3.5, 3.5, 3.5, 3.75, 4, 4.25, 4.5, 4.5, 4.5, 4.75, 5.25, 5.5, 5.75, 5.75, 5.75, 6, 6, 6, 6.25, 6.25, 6.25, 6.5, 6.5, 6.5, 6.75, 7, 7, 7, 7.5, 7.5, 7.75, 8, 8.25, 8.25, 8.25, 8.5, 8.75, 9, 9

Using calculator :

Sample mean, xbar = 5.71666

Sample standard deviation, s = 2.04

The test statistic :

(5.7166 - 8) ÷ (2.04/√(45))

-2.28 / 0.3041052

= - 7.5085

= - 7.51

Degree of freedom = 45 - 1 = 44

Pvalue(-7.51, 44) = 0.00001

α = 1% = 0.01

Since Pvalue < α ; we reject H0 and conclude that there is statistical significance that student at the school get less than 8 hours of sleep on average.