Respuesta :
Answer:
The value of t test statistics is -2.
Step-by-step explanation:
We are given that a study was conducted to determine whether UH students sleep fewer than 8 hours.
The study was based on a sample of 100 students. The sample mean number of hours of sleep was 7 hours and the sample standard deviation was 5 hours.
Let [tex]\mu[/tex] = mean number of hours UH students sleep.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 8 hours {means that UH students sleep more than or equal to 8 hours}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 8 hours {means that UH students sleep fewer than 8 hours}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean number of hours of sleep = 7 hours
s = sample standard deviation = 5 hours
n = sample of students = 100
So, test statistics = [tex]\frac{7-8}{\frac{5}{\sqrt{100} } }[/tex] ~ [tex]t_9_9[/tex]
= -2
Hence, the value of t test statistics is -2.
