Microsoft Word - ECON2025 Takehome Test.doc
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.
We shall investigate the following question: Does the random sample provide evidence that the second researcher is correct?
(a) If the null hypothesis is true, what would the sampling distribution of the mean number of hours of TV watched per week look like?
(b) Find the probability of randomly choosing a sample in which the average number of hours of TV watched was 24.2 or more.
(c) There's no hard and fast dividing line between P-values for which we reject the null hypothesis and those for which we feel the null hypothesis is plausible. But P =
2
0.05 and P = 0.01 are two commonly used thresholds. Under these guidelines, would you reject the null hypothesis?
(d) If the second researcher doubted the 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 as extreme or more extreme that 24.2 hours. Would you reject the null hypothesis in this case?
(e) 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?