Respuesta :
The correct answers to the question are:
A. b
B. c.
C. (1.486, 1.594)
d. b
A. why a large sample size is needed to calculate a confidence interval
This is because it would help to make the mean normal. This is given that the distribution for eating and drinking is not properly skewed.
B. The random sample of 972 is less than the population by 5 percent so it can be said to have satisfied the requirement. option c
C. sample size n = 972
mean = 1.54
sd = 0.65
1 - 0.99 = 0.01
Z0.01/2 = 2.58
The confidence interval would be gotten as
1.54 ± 2.58 ( 0.65/√972)
= 1.54 ± 2.58*0.021
= 1.54 - 0.054 , 1.54 + 0.054
= (1.486, 1.594)
d. The correct answer is b. The mean may differ given that the interval is about those that are 15 or more.
Read more on confidence interval here:
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Complete question
5. A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 969 people age 15 or older, the mean amount of time spend eating or drinking per day is 1.85 hours with a standard deviation of 0.67 hours. Complete parts (a) through (d) below.
A). A histogram of time spends 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. Since the distribution of time spent eating and drinking each day is not normally distributed (skewed right), the sample must be larger so that the distribution of the sample mean will be approximately normal.
c. Since the distribution of time spent eating and drinking each day is normally distributed, the sample must be larger so that the distribution of the sample mean will be approximately normal.
d.The distribution of the sample mean will never 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 less than 10% of the population.
b. The sample size is greater than 5% 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 the time Americans age 15 or older spend eating and drinking each day. Select the correct choice and fill in the blanks.
a. There is a 99% probability that the mean amount of time spent eating and drinking per day is between _____ and _____ hours.
b. The nutritionist is 99% confident that the amount of time spent eating and drinking per day for any individual is between _____ and _____ hours.
c. The nutritionist is 99% confident that the mean amount of time spent eating and drinking per day is between _____ and _____ hours.
d. The requirements for conducting 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?
a. Yes; the interval is about the mean amount of time spend eating and drinking per day for people age 15 or older and can be used to find the mean amount of time spent eating and drinking per day for a 9 year olds.
b. No; the interval is about people age 15 or older. The mean amount of time spent eating and drinking per day for 9 years old may differ.
c. No; the interval is about individual time spent eating and drinking per day and cannot be use to fin the mean time spent eating and drinking per day for specific age.
d. Yes; the interval is about individual time spent eating and drinking 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)
