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

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

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 \\eq 8`

The test statistic is:

`t = (X - \mu)/((s)/(√(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 = (X - \mu)/((s)/(√(n)))`

`t = (7.3 - 8)/((2.6)/(√(101)))`

`t = -2.71`

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