Question Help

A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 1064 people age 15 orolder, the mean amount of time spent eating or drinking per day is 1.23 hours with a standard deviation of 0.62 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 normallydistributed, the sample must be large so that the distribution of the sample mean will be approximately normal.

B.

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

C.

The distribution of the sample mean will never 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 whythis, along with the fact that the data were obtained using a randomsample, satisfies the requirements for constructing a confidence interval.

A.

The sample size is greater than10% of the population.

B.

The sample size is greater than5% of the population.

C.

The sample size is less than10% of the population.

D.

The sample size is less than5% 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 answerboxes, ifapplicable, in your choice.

(Type integers or decimals rounded to three decimal places as needed. Use ascendingorder.)

A.

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.

B.

There is a 95% probability that the mean amount of time spent eating or drinking per day is between

nothing

and

nothing

hours.

C.

The nutritionist is 95% confident 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 a9-year-old spends eating and drinking eachday? 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 a9-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 for9-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 for9-year-olds.

E.

A confidence interval could not be constructed in part (c).