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.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.) (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 middleschool students is approximately normal. (Round your answer to nearest percent.)If the distribution of volunteer times is approximately normal and we assume the sample mean of x = 14.76 hours, and standard deviation of s = 16.54 hours are good approximations to thepopulation mean and standard deviation, we would expect that approximately 18.67% of volunteer times would be negative. Therefore, it is notreasonable to think thatthe distribution of volunteer times is approximately normal.(b) The sample size was not given in the paper, but the sample size was described as "large." Suppose that the sample size was 700. Explain why it is reasonable to use a one-sample t confidenceinterval to estimate the population mean even though the population distribution is not approximately normal. (Select all that apply.)It is reasonable to use a one-sample t confidence interval to estimate the population mean since the sample is representative of the population.It is reasonable to use a one-sample t confidence interval to estimate the population mean since the statistics came from a paper.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.It is reasonable to use a one-sample t confidence interval to estimate the population mean since the sample size is at most 30.(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 decimalplaces.)13.30316.217hrsInterpret the interval.

Given information Sample size n = 700 Sample mean x̅ = 14.76 hours Standard deviation s = 16.54…

Answered: The paper "The Effects of Adolescent…

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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.

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.)

(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 and we assume the sample mean of x = 14.76 hours, and standard deviation of s = 16.54 hours are good approximations to the
population mean and standard deviation, we would expect that approximately 18.67
% of volunteer times would be negative. Therefore, it is not
reasonable to think that
the distribution of volunteer times is approximately normal.
(b) The sample size was not given in the paper, but the sample size was described as "large." Suppose that the sample size was 700. 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.)
It is reasonable to use a one-sample t confidence interval to estimate the population mean since the sample is representative of the population.
It is reasonable to use a one-sample t confidence interval to estimate the population mean since the statistics came from a paper.
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.
It is reasonable to use a one-sample t confidence interval to estimate the population mean since the sample size is at most 30.
(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.)
13.303
16.217
hrs
Interpret the interval.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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