In June 2009, Harris Interactive conducted its Great Schools Survey. In this survey, the sample consisted of 1086 adults who were parents of school-aged children. The sample was selected in a way that makes it reasonable to regard it as representative of the population of parents of school-aged children. One question on the survey asked respondents how much time (in hours) per month they spent volunteering at their children’s school during the previous school year. The following summary statistics for time volunteered per month were given: n = 1086 x = 5.6 median = 1
a. What does the fact that the mean is so much larger than the median tell you about the distribution of time spent volunteering per month?
b. Based on your answer to Part (a), explain why it is not reasonable to assume that the population distribution of time spent volunteering is approximately normal.
c. Explain why it is appropriate to use the t confidence interval to estimate the mean time spent volunteering for the population of parents of school-aged children even though the population distribution is not approximately normal.
d. Suppose that the sample standard deviation was s = 5.2. Compute and interpret a 98% confidence interval for m, the mean time spent volunteering for the population of parents of school-aged children.