Respuesta :
Answer:
The t-statistic that Jacob calculates is [tex]t = -2.71[/tex]
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:
[tex]H_0: \mu = 8[/tex]
At the alternative hypothesis, we test if the mean is different of 8 hours, that is:
[tex]H_1: \mu \neq 8[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] 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 [tex]\mu = 8[/tex]
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 [tex]n = 101, X = 7.3, s = 2.6[/tex]
What is the t-statistic that Jacob calculates?
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{7.3 - 8}{\frac{2.6}{\sqrt{101}}}[/tex]
[tex]t = -2.71[/tex]
The t-statistic that Jacob calculates is [tex]t = -2.71[/tex]
