Question

A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 994 people age 15 or older, the mean amount of time spent eating or drinking per day is 1.53 hours with a standard deviation of 0.66 hour.

). 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 interval for the mean time spent eating and drinking each day. 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. B. 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. C. The distribution of the sample mean will never be approximately normal. D. The distribution of the sample mean will always 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. A. The sample size is less than 10% of the population. B. The sample size is less than 5% of the population. C. The sample size is greater than 10% of the population. D. The sample size is greater than 5% of the population.

(c) Determine and interpret a 90% confidence interval 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.) A. The nutritionist is 90 % confident that the amount of time spent eating or drinking per day for any individual is between blank and blank hours. B. There is a 90 % probability that the mean amount of time spent eating or drinking per day is between nothing and nothing hours. C. The nutritionist is 90 % confident that the mean amount of time spent eating or drinking per day is between blank and blank hours. D. The requirements for constructing a confidence interval 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. 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. B. 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. C. Yes; the interval 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. D. No; the interval is about individual time spent eating or drinking per day and cannot be used to find the mean time spent eating or drinking per day for specific age. E. A confidence interval could not be constructed in part (c).

Answer 1

A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 994 people age 15 or older, the mean amount of time spent eating or drinking per day is 1.53 hours with a standard deviation of 0.66 hour.
A). A histogram of time spends eating and drinking each day is skewed right. Use this result to explain why a large sample size is needed to construct a confidence interval for the mean time spent eating and drinking each day.
a. The distribution of the sample mean will always be approximately normal.
b. Since the distribution of time spent eating and drinking each day is not normally distributed (skewed right), the sample must be larger so that the distribution of the sample mean will be approximately normal.
c. Since the distribution of time spent eating and drinking each day is normally distributed, the sample must be larger so that the distribution of the sample mean will be approximately normal.	Correct	Since the distribution is skewed right (not normally distributed) the sample must be large so that the distribution of the same mean will be approximately normal.
d.The distribution of the sample mean will never be approximately normal.
B). In 2010, there were over 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.
a. The sample size is less than 10% of the population.
b. The sample size is greater than 10% of the population.
c. The sample size is less than 5% of the population.	Correct	The sample size is less than 5% of the population (n < 0.05N)
d. The sample size is greater than 5% of the population.
C). Determine and interpret a 95% confidence interval for the mean amount of the time Americans age 15 or older spend eating and drinking each day. Select the correct choice and fill in the blanks.
a. There is a 95% probability that the mean amount of time spent eating and drinking per day is between what hours.
b. The nutritionist is 95% confident that the amount of time spent eating and drinking per day for any individual is between what hours.
c. The nutritionist is 95% confident that the mean amount of time spent eating and drinking per day is between what hours.	Correct	Which means the nutritionist can be 95% confident that the mean amount of time Americans spend eating/drinking per day is between 1.50 and 1.56 hours
d. The requirements for conducting a confidence interval are not satisfied.
Mean	1.53	90% Confidence Interval: 1.53 ± 0.0344
SD	0.66	(1.5 to 1.56)
N	994	"With 90% confidence the population mean is between 1.5 and 1.56, based on 994 samples."
C -level	90%	Short Styles:
Confidence Interval	0.034433249	1.53 (90% CI 1.5 to 1.56)
Maximum  = 1.53 + 0.0344	1.56	1.53, 90% CI [1.5, 1.56]
Minimum = 1.53 - 0.0344	1.50	Margin of Error: 0.0344
		(to more digits: 0.03443)
D). Could the interval be used to estimate the mean amount of time a 9 year old spends eating and drinking each day?
a. Yes; the interval is about the mean amount of time spend eating and drinking per day for people age 15 or older and can be used to find the mean amount of time spent eating and drinking per day for a 9 year olds.
b. No; the interval is about people age 15 or older. The mean amount of time spent eating and drinking per day for 9 years old may differ.	Correct	No, the interval is about people age 15 and older. The amount for 9-year-olds could easily be very different.
c. No; the interval is about individual time spent eating and drinking per day and cannot be use to fin the mean time spent eating and drinking per day for specific age.
d. Yes; the interval is about individual time spent eating and drinking per day and can be used to find the mean amount of time a 9 year old spends eating and drinking each day.
e. A confidence interval could not be constructed in part (c)