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

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 $\mu$ = 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. =  $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$  ~ $t_n_-_1$

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  =  $\frac{7-8}{\frac{5}{\sqrt{100} } }$  ~ $t_9_9$

                              =  -2

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