Chapter 24, Problem 30E

(a)

To determine

To explain what “statistically significant” means in this context.

Explanation of Solution

In this question, we are comparing science scores for students who had home internet access to the scores of those who did not. They reported that the differences are statistically significant.Thus, "Significantly significant" means that the difference between the results in $1996$ and the results in 2000 are so larger that they are unlikely to be due to chance.

(b)

To determine

To explain what type of error does the researchers commit.

Answer to Problem 30E

It is a Type II error.

Explanation of Solution

In this question, we are comparing science scores for students who had home internet access to the scores of those who did not. They reported that the differences are statistically significant. So, it is given in exercise $29$ that we have rejected the null hypothesis. Thus, we know that the errors are as:

Type I error is that when we fail to reject the null hypothesis, when it is true. And Type II error is when we reject the null hypothesis when it is false. So, if we wrongly rejected the null hypothesis then we thus made Type II error.

(c)

To determine

To explain does this prove that using internet at home can improve a student’s performance in science.

Answer to Problem 30E

No, it does not prove.

Explanation of Solution

In this question, we are comparing science scores for students who had home internet access to the scores of those who did not. They reported that the differences are statistically significant. Thus, this does not prove that using internet at home can improve a student’s performance in science because the study is an observational study which cannot prove causation, since the improvement could be due to lurking variables.A lurking variable is a variable that has an important effect on the relationship among the variables in a study but is not one of the explanatory variables studied.If we want to prove causation, then we require an experiment.