A nutritionist wants to determine how much time nationallypeople spend eating and drinking. Suppose for a random sampleof
1062 people age 15 or? older, the mean amount of time spent eatingor drinking per day is
1.07 hours with a standard deviation of 0.65 hour. Complete parts?(a) through ?(d) below.
?(a) A histogram of time spent eating and drinking each day isskewed right. Use this result to explain why a large sample size isneeded to construct a confidence interval for the mean time spenteating and drinking each day.
A. The distribution of the sample mean will never beapproximately normal.
B. Since the distribution of time spent eating and drinking eachday is not normally distributed? (skewed right), the sample must belarge so that the distribution of the sample mean will beapproximately normal.
C. The distribution of the sample mean will always beapproximately normal.
D. Since the distribution of time spent eating and drinking eachday is normally? distributed, the sample must be large so that thedistribution of the sample mean will be approximately normal.
?(b) In? 2010, there were over 200 million people nationally age15 or older. Explain why? this, along with the fact that the datawere obtained using a random? sample, satisfies the requirementsfor constructing a confidence interval.
A. The sample size is less than? 5% of the population.
B. The sample size is greater than? 10% of the population.
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 90?% confidence interval for themean amount of time Americans age 15 or older spend eating anddrinking 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 asneeded. Use ascending? order.)
A.The nutritionist is 90?% confident that the amount of timespent eating or drinking per day for any individual is between ____and ____hours.
B.There is a 90?% probability that the mean amount of time spenteating or drinking per day is between ____ and ____ hours.
C.The nutritionist is 90?% confident that the mean amount oftime spent eating or drinking per day is between ____ and ____hours.
D.The requirements for constructing a confidence interval arenot satisfied.
(d) Could the interval be used to estimate the mean amount oftime a? 9-year-old spends eating and drinking each? day?Explain.
A. No; the interval is about individual time spent eating ordrinking per day and cannot be used to find the mean time spenteating or drinking per day for specific age.
B. No; the interval is about people age 15 or older. The meanamount of time spent eating or drinking per day for? 9-year-oldsmay differ.
C. ?Yes; the interval is about the mean amount of time spenteating or drinking per day for people people age 15 or older andcan be used to find the mean amount of time spent eating ordrinking per day for? 9-year-olds.
D. Yes; the interval is about individual time spent eating ordrinking 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).
