Question

4. A sociologist cites a study showing that, in a particular parish, the amount of time preschool children ages 3–5 spend watching TV is 22.6 hours per week, with a standard deviation of 6.1 hours.

A second researcher doubts these findings, believing that the actual figure is higher. To attempt to resolve the question, a simple random sample of 60 preschool children is chosen, and their TV watching habits are measured by having their parents keep a daily log of television watching. The children in the sample watched an average of 24.2 hours of TV per week. Does the random sample provide evidence that the second researcher is correct?

(a) There’s no hard and fast dividing line between significance levels for which we reject the null hypothesis and those for which we feel the null hypothesis is plausible. But a = 0.05 and a = 0.01 are two commonly used thresholds. Under these different thresholds, would you reject the null hypothesis of the second researcher?

(b) If the second researcher doubted his findings but had no preconceived idea of whether they were too high or too low, we should instead ask for the probability of randomly choosing a sample in which the average number of hours of TV watched was not as extreme as, or more extreme than 22.6 hours. Would you reject the null hypothesis in this case? Compare at significance levels of a = 0.05 and a = 0.01 respectively.

(c) Would a larger sample with the same mean of 24.2 have provided stronger, weaker or the same evidence of a difference from a mean of 22.6? Why?

Answer 1