Question

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.

1. What is the value of the test statistic?
a. 0.5
b. 5.0
c. 1.2
d. -5.0

Answer 1

The value of t test statistics is -2.

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
`\mu` = mean number of hours UH students sleep.

So, Null Hypothesis,
`H_0` :
`\mu \geq` 8 hours {means that UH students sleep more than or equal to 8 hours}

Alternate Hypothesis,
`H_A` :
`\mu` < 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. =
`(\bar X-\mu)/((s)/(√(n) ) )` ~
`t_n_-_1`

where,
`\bar X` = sample mean number of hours of sleep = 7 hours

s = sample standard deviation = 5 hours

n = sample of students = 100

So, test statistics =
`(7-8)/((5)/(√(100) ) )` ~
`t_9_9`

= -2

Hence, the value of t test statistics is -2.