A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 911 people age 15 or​ older, the mean amount of time spent eating or drinking per day is 1.68 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 normally​ distributed, 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 never be approximately normal.   C. The distribution of the sample mean will always be approximately normal. Your answer is not correct.   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. This is the correct answer. ​(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 less than​ 5% of the population. This is the correct answer.   B. The sample size is less than​ 10% of the population.   C. The sample size is greater than​ 5% of the population. Your answer is not correct.   D. The sample size is greater than​ 10% of the population. ​(c) Determine and interpret a 90​% 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 90​% 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 90​% probability that the mean amount of time spent eating or drinking per day is between nothing and nothing hours.   C. The nutritionist is 90​% 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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of
911
people age 15 or​ older, the mean amount of time spent eating or drinking per day is
1.68
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 normally​ distributed, 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 never be approximately normal.
 
C.
The distribution of the sample mean will always be approximately normal.
Your answer is not correct.
 
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.
This is the correct answer.
​(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 less than​ 5% of the population.
This is the correct answer.
 
B.
The sample size is less than​ 10% of the population.
 
C.
The sample size is greater than​ 5% of the population.
Your answer is not correct.
 
D.
The sample size is greater than​ 10% of the population.
​(c) Determine and interpret a
90​%
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
90​%
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
90​%
probability that the mean amount of time spent eating or drinking per day is between
nothing
and
nothing
hours.
 
C.
The nutritionist is
90​%
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.
 
 
 
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