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?

The t-statistic that Jacob calculates is

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:

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

The test statistic is:

In which X is the sample mean, 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

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

What is the t-statistic that Jacob calculates?

The t-statistic that Jacob calculates is

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

25/6 hope it : )

step-by-step explanation: