A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample

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A nutritionist wants to determine how much time nationally
people spend eating and drinking. Suppose for a random sample
of 1037 people age 15 or​ older, the mean amount of
time spent eating or drinking per day is 1.99 hours
with a standard deviation of 0.54 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. The distribution of the sample mean will never be
approximately normal.
B. The distribution of the sample mean will always be
approximately normal.
C. 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.
D. 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.
A. The sample size is greater than​ 5% of the
population.
B. The sample size is less than​ 10% of the
population.
C. The sample size is less than​ 5% of the
population.
D. The sample size is greater than​ 10% 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.
​(Type integers or decimals rounded to three decimal places as
needed. Use ascending​ order.)
A.The nutritionist is 99​% confident that the mean
amount of time spent eating or drinking per day is
between _____ and _____ hours.
B.The nutritionist is 99​% confident that the amount
of time spent eating or drinking per day for any individual is
between _____ and _____ hours.
C.There is a 99​% probability that the mean amount of
time spent eating or drinking per day is between _____ and
_____ 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).