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 $TypeII$error is not to reject that the mean number of hours of sleep LTCC students get per night is at least seven when,

in fact, the mean number of hours

a. is more than seven hours.

b. is at most seven hours.

c. is at least seven hours.

d. is less than seven hours.

Short answer

d. is less than seven hours.

Step-by-step solution

Given information: 

$$\begin{gathered} \alpha (significancelevel)=0.05 \\ n=22 \\ \sigma =1.93 \\ \overline{x}=7.24 \\ Also,fromtheproblem,wecanstatethenullandalternativehypothesesas: \\ {H}_0:\mu \ge 7;H_a:\mu <7 \end{gathered}$$

From this information, we can find out the p-value.

Solution: 

The correct option is d.

From this information, we can find out the p-value to be greater than significance value.

Since the p-value is greater than 0.05 we can reject the null hypothesis.

The null hypothesis is false.

And $TypeII$error, therefore, occurs when we do not reject the null hypothesis even when it is false.