Question

Previously, an organization reported that teenagers spent $4.5$ hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was $4.75$ hours with a sample standard deviation of $2.0$. Conduct a hypothesis test, the $TypeI$error is:

a. to conclude that the current mean hours per week is higher than $4.5$, when in fact, it is higher

b. to conclude that the current mean hours per week is higher than $4.5$, when in fact, it is the same

c. to conclude that the mean hours per week currently is $4.5$, when in fact, it is higher

d. to conclude that the mean hours per week currently is no higher than , when in fact, it is not higher

Short answer

The correct option is b which says that the current mean hours per week is higher than $4.5$, when in fact, it is the same.

Step-by-step solution

Given information

$$\begin{gathered} n=15 \\ \overline{x}=4.75 \\ \sigma =2 \\ Wecanwritefromtheproblemthat: \\ {H}_0:\mu =4.5;H_a:\mu >4.5 \end{gathered}$$

We have to describe a Type I error in this solution.

Explanation

The correct option is b.

The null hypothesis states that the teenagers spent $4.5$ hours per week, on average, on the phone.

When we find out the p-value the null hypothesis comes out to be true.

So, for a Type I error we have to reject the Null Hypothesis while being true which gives us option b as the answer.