Question
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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
1.52
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.
The distribution of the sample mean will always be approximately normal.

B.
The distribution of the sample mean will never be approximately normal.

C.
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.

D.
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) 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​ 5% of the population.

B.
The sample size is less than​ 5% of the population.

C.
The sample size is less than​ 10% of the population.

D.
The sample size is greater than​ 10% of the population.
​(c) Determine and interpret a
95%
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
95%
confident that the mean amount of time spent eating or drinking per day is between
nothing
and
nothing
hours.

B.
The nutritionist is
95%
confident that the amount of time spent eating or drinking per day for any individual is between
nothing
and
nothing
hours.

C.
There is a
95%
probability that the mean amount of time spent eating or drinking per day is between
nothing
and
nothing
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.
​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.

B.
​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.

C.
​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.

D.
​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.

E.
A confidence interval could not be constructed in part

(c) Determine and interpret a
95%
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
95%
confident that the mean amount of time spent eating or drinking per day is between
nothing
and
nothing
hours.

B.
The nutritionist is
95%
confident that the amount of time spent eating or drinking per day for any individual is between
nothing
and
nothing
hours.

C.
There is a
95%
probability that the mean amount of time spent eating or drinking per day is between
nothing
and
nothing
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.
​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.

B.
​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.

C.
​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.

D.
​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.

E.
A confidence interval could not be constructed in part
​(c).
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Step 1

Hello! As you have posted 4 sub parts, we are answering the first 3 sub-parts.  In case you require the unanswered parts also, kindly re-post that parts separately.

Step 2

a)

Central Limit Theorem:

If the sample is selected from the population with finite mean and standard deviation, then the distribution of sample means follows normal distribution as sample size increases with regardless of population distribution.

From the given information, the histogram of time spent eating and drinking each day is skewed right and the sample size is large. From the central limit theorem, the sample mean follows normal distribution.

Hence, the correct option is “C. 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”.

Step 3

b)

Requirement for constructing the confidence interval:

For constructing the confidence interval, the sample size is less than 5% of the population size.

...

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