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 Type I 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 4.5, when in fact, it is not higher

Answer 1

Answer:

Type I error is : to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same.

Step-by-step explanation:

We are given that 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. For this 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 hours.

Let Null Hypothesis, $H_0$ : $\mu \leq$ 4.5 hours {means that the current mean hours per week is less than or equal to 4.5}

Alternate Hypothesis, $H_1$ : $\mu$ > 4.5 hours {means that the current mean hours per week is higher than 4.5}

Now, Type I error states that : Probability of rejecting null hypothesis given the fact that it was true or Rejecting the true null hypothesis.

So, according our question;

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