Question

Jacob knows that the adult population gets, on average, eight hours of sleep each night. A hypothesis test can help him see if college students are different from the adult population. From a sample of 101 students, Jacob tabulated that his sample of students got an average of 7.3 hours of sleep each night, with a standard deviation of 2.6.
Required:
What is the t- statistic that Jacob calculates?

Answer 1

Answer:

The t-statistic that Jacob calculates is $t = -2.71$

Step-by-step explanation:

Jacob knows that the adult population gets, on average, eight hours of sleep each night. A hypothesis test can help him see if college students are different from the adult population.

At the null hypothesis, we test if the mean is of 8 hours, that is:

$H_0: \mu = 8$

At the alternative hypothesis, we test if the mean is different of 8 hours, that is:

$H_1: \mu \neq 8$

The test statistic is:

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

8 is tested at the null hypothesis:

This means that $\mu = 8$

From a sample of 101 students, Jacob tabulated that his sample of students got an average of 7.3 hours of sleep each night, with a standard deviation of 2.6.

This means that $n = 101, X = 7.3, s = 2.6$

What is the t-statistic that Jacob calculates?

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{7.3 - 8}{\frac{2.6}{\sqrt{101}}}$

$t = -2.71$

The t-statistic that Jacob calculates is $t = -2.71$