Answer:
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.
