Null Hypothesis

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

what do i have to do in order to figure this out.

Answer 1

In this experiment the hypotheses are:

 

H₀: μ = 4.5 vs H_A: μ > 4.5

 

Type I error is defined as rejecting H₀ when H₀ is true.

 

Plugging in our hypotheses gives:

 

Conclude μ > 4.5 when in reality μ = 4.5.

 

This is answer b.

 

 

The other answers are wrong. For example, choice c is a Type II error. Choices a,d indicate making the correct conclusion about the population.