A nutritionist wants to determine how much time nationally p

A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 928 people age 15 or older, the mean amount of time spent eating or drinking per day is 1.03 hours with a standard deviation of 0.66 hour.

A. 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.

1. The sample size is greater than 5% of the population

2. The sample size is greater than 10% of the population

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

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

B. Determine and interpret a 99% confidence interval for the mean amount of time Americans age 15 or older spend eating and drinking each day.

1. The nutritionist is 99% confident that the mean amount of time spent eating or drinking per day is between _____ and ______ hours.

2. There is a 99% probability that the mean amount of time spent eating or drinking per day for an individual is between ___ and ___ hours.

3. The nutritionist is 99% confident that the amount of time spent eating or drinking per day for an individual is between ____ and ____ hours.

4. The requirements for constructing a confidence interval are not satisfied.

Solution

A.
1. The sample size is greater than 5% of the population
If the sample size is more than 5% of the population size and the sampling is done without replacement, then a correction needs to be made to the standard error of the means.

B.
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=1.03
Standard deviation( sd )=0.66
Sample Size(n)=928
Confidence Interval = [ 1.03 ± t a/2 ( 0.66/ Sqrt ( 928) ) ]
= [ 1.03 - 2.581 * (0.022) , 1.03 + 2.581 * (0.022) ]
= [ 0.974,1.086 ]
The nutritionist is 99% confident that the mean amount of time spent eating or drinking per day is between 0.974 and 1.086 hours.