Solutions

1. This statement confuses the variable (the question) with the parameter (a number). The single number that we are interested in here is the mean amount of time.

2. These hypotheses do not make statements about the parameter.

3. The symbol pertains to a proportion, but since we have a quantitative variable here (amount of time spent watching television), the parameter is a mean, denoted by .

4. The hypotheses should always be statements about the unknown population parameter, here. The symbol is reserved for the sample mean and should not appear in a hypothesis statement. The observed value of the sample mean also should not appear in a hypothesis statement.

5. This calculation forgets to divide by the square root of the sample size in the denominator, using the sample standard deviation instead of the standard error for .

6. The numerator in this calculation subtracts 2, perhaps thinking of hours per day instead of hours per week, where it should subtract 14.

7. This is a tempting conclusion to draw, but it sounds too much like “accepting” the null hypothesis. Because the p-value was not terribly small here, we do not reject the null hypothesis, but that does not mean that we accept it. It is better to say we do not have convincing evidence that children in the population spend more than an average of two hours per day watching television.

8. This conclusion is wrong because of the phrase “all children.” A very small p-value would lead us to conclude that the mean time watching television exceeds two hours per day. But the average exceeding two does not mean that every child’s value exceeds two.

9. The word “most” instead of “all” makes this conclusion more palatable than the previous one, but this statement is wrong for the same reason. Just because the mean value exceeds two, we cannot conclude that most individual values exceed two. Recall from your earlier study of the mean that with a skewed distribution it’s possible for a fairly small percentage of values to exceed the mean.