A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 1077 people age 15 or older, the mean amount of time spent eating or drinking per day is 1.66 hours with a standard deviation of 0.62 hour. Complete parts (a) through (d) below. (a) A histogram of time spent eating and drinking each day is skewed right. Use this result to explain why a large sample size is needed to construct a confidence intenal for the mean time spent eating and drinking each day. O A. Since the distribution of time spent eating and drinking each day is normally distributed, the sample must be large so that the distribution of the sample mean will be approximately normal. O B. The distribution of the sample mean will always be approximately normal. OC. The distribution of the sample mean will never be approximately normal. OD. Since the distribution of time spent eating and drinking each day is not normally distributed (skewed right), the sample must be large so that the distribution of the sample mean will be approximately normal. (b) There are more than 200 million people nationally age 15 or older. Explain why this, along with the fact that the data were obtained using a random sample, satisfies the requirements for constructing a confidence interval. O A. The sample size is less than 10% of the population. OB. The sample size is less than 5% of the population. OC. The sample size is greater than 10% of the population. OD. The sample size is greater than 5% of the population. (c) Determine and interpret a 90% confidence intenval for the mean amount of time Americans age 15 or older spend eating and drinking each day. Select the correct choice below and fill in the answer boxes, if applicable, in your choice. (Type integers or decimals rounded to three decimal places as needed. Use ascending order.) O A. The nutritionist is 90% confident that the amount of time spent eating or drinking per day for any individual is between and hours. OB. There is a 90% probability that the mean amount of time spent eating or drinking per day is between and hours. OC. The nutritionist is 90% confident that the mean amount of time spent eating or drinking per day is between and hours. OD. The requirements for constructing a confidence intenal are not satisfied. (d) Could the interval be used to estimate the mean amount of time a 9-year-old spends eating and drinking each day? Explain. O A. No; the interval is about people age 15 or older. The mean amount of time spent eating or drinking per day for 9-year-olds may differ. O B. Yes; the intenval is about individual time spent eating or drinking per day and can be used to find the mean amount of time a 9-year-old spends eating and drinking each day. OC. No; the intenval is about individual time spent eating or drinking per day and cannot be used to find the mean t OD. Yes; the interval is about the mean amount of time spent eating or drinking per day for people people age 15 or older and can be used to find the mean amount of time spent eating or drinking per day for 9-year-olds. OE. A confidence interval could not be constructed in part (c). spent eating or drinking per day for specific age.

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 + ...