Question

It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of $22$LTCC Intermediate Algebra students generated a mean of $7.24$hours with a standard deviation of $1.93$hours. At a level of significance of $5\%$, do LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average? The distribution to be used for this test is $\overline{X}~$

$a.N\left(7.24,\frac{1.93}{\sqrt{22}}\right)$

$b.N(7.24,1.93)$

$c.t_{22}$

$d.t_{21}$

Short answer

We use a Student$t$-distribution with $n-1$degrees of freedom i.e. $\overline{X}~t_{21}$.

Step-by-step solution

Student's t-distribution.

When we are testing a population means and when the population standard deviation is unknown we use a Student's $t$-distribution.

Using t21

Because in this test sample size is $n=22$, we use a Student's t-distribution with $n-1$degrees of freedom i.e.

$\overline{X}~t_{21}$