A nutritionist wants to determine how much time nationally people spend eating a
ID: 3353454 • Letter: A
Question
A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 978 people age 15 or older, the mean amount of time spent eating or drinking per day is 1.14 hours with a standard deviation of 0.59 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 interval for the mean time spent eating and drinking each day. A. 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. Your answer is correct. B. 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. 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) 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 greater than 10% of the population. B. The sample size is less than 5% of the population. Your answer is correct. C. The sample size is less than 10% of the population. D. The sample size is greater than 5% of the population. (c) Determine and interpret a 99 % 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. There is a 99 % probability that the mean amount of time spent eating or drinking per day is between nothing and nothing hours. B. The nutritionist is 99 % confident that the amount of time spent eating or drinking per day for any individual is between nothing and nothing hours. C. The nutritionist is 99 % confident that the mean amount of time spent eating or drinking per day is between 1.091 and 1.189 hours. Your answer is correct. 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. 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. B. 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. C. 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. D. 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. E. A confidence interval could not be constructed in part (c). Click to select your answer and then click Check Answer.
Explanation / Answer
Answer:
A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 978 people age 15 or older, the mean amount of time spent eating or drinking per day is 1.14 hours with a standard deviation of 0.59 hour. Complete parts (a) through (d) below.
Answer: A. 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. 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.
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) 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 greater than 10% of the population.
Answer: B. The sample size is less than 5% of the population. Your answer is correct.
C. The sample size is less than 10% of the population.
D. The sample size is greater than 5% of the population.
(c) Determine and interpret a 99 % 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. There is a 99 % probability that the mean amount of time spent eating or drinking per day is between nothing and nothing hours.
B. The nutritionist is 99 % confident that the amount of time spent eating or drinking per day for any individual is between nothing and nothing hours.
Answer: C. The nutritionist is 99 % confident that the mean amount of time spent eating or drinking per day is between 1.091 and 1.189 hours. Your answer is correct.
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. 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.
Answer: B. 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.
C. 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
. D. 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.
E. A confidence interval could not be constructed in part (c).
Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation
0.59
Sample Mean
1.14
Sample Size
978
Confidence Level
99%
Intermediate Calculations
Standard Error of the Mean
0.01886612
Degrees of Freedom
977
t Value
2.5809
Interval Half Width
0.0487
Confidence Interval
Interval Lower Limit
1.091
Interval Upper Limit
1.189
Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation
0.59
Sample Mean
1.14
Sample Size
978
Confidence Level
99%
Intermediate Calculations
Standard Error of the Mean
0.01886612
Degrees of Freedom
977
t Value
2.5809
Interval Half Width
0.0487
Confidence Interval
Interval Lower Limit
1.091
Interval Upper Limit
1.189
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