Question

A nutritionist wants to determine how much time nationally people spend eating and drinking soup for a random sample of 1025 people age 15 or older. The mean amount of time spent eating or drinking per day is 16 hours with a standard deviation of 0.68 hours. Complete parts (a) through (d) below: (a) Histogram of time spent eating and drinking each day 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. Since the distribution of time spent eating and drinking each day is highly skewed right, a large sample size is needed to minimize the margin of error and ensure that only the peak of the sampling distribution captures the confidence interval. Additionally, a large sample size is needed to ensure that the distribution of the sample mean is 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. The sample size is greater than 5% of the population, which satisfies the requirement for constructing a confidence interval. (c) Determine and interpret a 99% confidence interval for the mean amount of time Americans age 15 or older spend eating and drinking each day. The nutritionist is 99% confident that the amount of time spent eating or drinking per day for any individual is between [insert lower bound] and [insert upper bound] hours. There is a 99% probability that the mean amount of time spent eating or drinking per day is between [insert lower bound] and [insert upper bound] hours. The nutritionist is 99% confident that the mean amount of time spent eating or drinking per day is between [insert lower bound] and [insert upper bound] hours. (d) Could the interval be used to estimate the mean amount of time a 9-year-old spends eating and drinking each day? Explain. 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.

Name: a nutritionist wants to determine how much time nationally people spend eating and drinking suppe ose for random sampi of 1025 people age 15 or older the mean amount of time spent eating or 72634
Uploaded: 2023-09-06T03:16:25-08:00
Duration: 4 min 55 s
Channel: Jerelyn Nevil
Description: a nutritionist wants to determine how much time nationally people spend eating and drinking suppe ose for random sampi of 1025 people age 15 or older the mean amount of time spent eating or 72634

(a) Histogram of time spent eating and drinking each day 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.

Since the distribution of time spent eating and drinking each day is highly skewed right, a large sample size is needed to minimize the margin of error and ensure that only the peak of the sampling distribution captures the confidence interval. Additionally, a large sample size is needed to ensure that the distribution of the sample mean is 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.

The sample size is greater than 5% of the population, which satisfies the requirement for constructing a confidence interval.

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

The nutritionist is 99% confident that the amount of time spent eating or drinking per day for any individual is between [insert lower bound] and [insert upper bound] hours.

There is a 99% probability that the mean amount of time spent eating or drinking per day is between [insert lower bound] and [insert upper bound] hours.

The nutritionist is 99% confident that the mean amount of time spent eating or drinking per day is between [insert lower bound] and [insert upper bound] hours.

(d) Could the interval be used to estimate the mean amount of time a 9-year-old spends eating and drinking each day? Explain.

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.

Added by Todd C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Jerelyn Nevil

09/06/2023

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This is because a large sample size helps to reduce the impact of outliers and extreme values, which can distort the shape of the sampling distribution and affect the accuracy of the confidence interval. (b) The correct answer is: The sample size is greater than Show more…

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A nutritionist wants to determine how much time nationally people spend eating and drinking soup for a random sample of 1025 people age 15 or older. The mean amount of time spent eating or drinking per day is 16 hours with a standard deviation of 0.68 hours. Complete parts (a) through (d) below: (a) Histogram of time spent eating and drinking each day 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. Since the distribution of time spent eating and drinking each day is highly skewed right, a large sample size is needed to minimize the margin of error and ensure that only the peak of the sampling distribution captures the confidence interval. Additionally, a large sample size is needed to ensure that the distribution of the sample mean is 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. The sample size is greater than 5% of the population, which satisfies the requirement for constructing a confidence interval. (c) Determine and interpret a 99% confidence interval for the mean amount of time Americans age 15 or older spend eating and drinking each day. The nutritionist is 99% confident that the amount of time spent eating or drinking per day for any individual is between [insert lower bound] and [insert upper bound] hours. There is a 99% probability that the mean amount of time spent eating or drinking per day is between [insert lower bound] and [insert upper bound] hours. The nutritionist is 99% confident that the mean amount of time spent eating or drinking per day is between [insert lower bound] and [insert upper bound] hours. (d) Could the interval be used to estimate the mean amount of time a 9-year-old spends eating and drinking each day? Explain. 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.