The paper "The Effects of Adolescent Volunteer Activities on the Perception of Local Society and Community Spirit Mediated by Self-Conception"+ describes a survey of a large representative sample of middle school children in South Korea. One question in the survey asked how much time per year the children spent in volunteer activities. The sample mean was 14.76 hours and the sample standard deviation was 16.54 hours. LO USE SALT (a) Based on the reported sample mean and sample standard deviation, explain why it is not reasonable to think that the distribution of volunteer times for the population of South Korean middle school students is approximately normal. (Round your answer to nearest percent.) If the distribution of volunteer times is approximately normal, for the sample standard deviation of s = 16.54 hours and the sample mean of x = 14.76 hours, approximately | 0.1867 * % of volunteer times would be negative. Therefore, it is v X reasonable to think that the distribution of volunteer times is approximately normal. ---Select-- is not (b) The sample size was not given in the paper, but the sample size was described as large. Suppose that the sample size was 600. Explain why it is reasonable to use a one-sample t confidence interval to estimate the population mean even though the population distribution is not approximately normal. (Select all that apply.) O It is reasonable to use a one-sample t confidence interval to estimate the population mean since the statistics came from a paper. O It is reasonable to use a one-sample t confidence interval to estimate the population mean since the sample size is at most 30. 4 It is reasonable to use a one-sample t confidence interval to estimate the population mean since the sample size is at least 30. It is reasonable to use a one-sample t confidence interval to estimate the population mean since all of the middle school children in South Korea were surveyed. O It is reasonable to use a one-sample t confidence interval to estimate the population mean since the sample is representative of the population. X (c) Calculate a 95% confidence interval (in hours) for the mean number of hours spent in volunteer activities per year for South Korean middle school children. (Round your answers to three decimal places.) 13.437 X 16.083 * ) hrs Interpret the interval. We are 95% confident that the true mean number of hours spent in volunteer activities per year for South Korean middle school children falls within this interval. There is a 95% chance that the number of hours spent in volunteer activities per year for South Korean middle school children falls within this interval. There is a 95% chance that the true mean number of hours spent in volunteer activities per year for South Korean middle school children falls directly in the middle of this interval. There is a 95% chance that the number of hours spent in volunteer activities per year for South Korean middle school children falls directly in the middle of this interval. We are 95% confident that the number of hours spent in volunteer activities per year for South Korean middle school children falls within this interval. X
