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7.81 Household Size. In Example 7.9 on page 322, we conducted a simulation to check the plausibility of the central limit theorem. The variable under consideration there is household size, and the population consists of all U.S. households. A frequency distribution for household size of U.S. households is presented in Table 7.7. a. Suppose that you simulate 1000 samples of four households each, determine the sample mean of each of the 1000 samples, and ob- tain a histogram of the 1000 sample means. Would you expect the histogram to be bell shaped? Explain your answer. b. Carry out the tasks in part (a) and note the shape of the histogram. c. Repeat parts (a) and (b) for samples of size 10. d. Repeat parts (a) and (b) for samples of size 100.

7.81 Household Size. In Example 7.9 on page 322, we conducted a simulation to check the plausibility of the central limit theorem. The variable under consideration there is household size, and the population consists of all U.S. households. A frequency distribution for household size of U.S. households is presented in Table 7.7. a. Suppose that you simulate 1000 samples of four households each, determine the sample mean of each of the 1000 samples, and ob- tain a histogram of the 1000 sample means. Would you expect the histogram to be bell shaped? Explain your answer. b. Carry out the tasks in part (a) and note the shape of the histogram. c. Repeat parts (a) and (b) for samples of size 10. d. Repeat parts (a) and (b) for samples of size 100.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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**7.81 Household Size** In Example 7.9 on page 322, we conducted a simulation to check the plausibility of the central limit theorem. The variable under consideration is household size, and the population consists of all U.S. households. A frequency distribution for household size of U.S. households is presented in Table 7.7. a. Suppose that you simulate 1000 samples of four households each, determine the sample mean of each of the 1000 samples, and obtain a histogram of the 1000 sample means. Would you expect the histogram to be bell-shaped? Explain your answer. b. Carry out the tasks in part (a) and note the shape of the histogram. c. Repeat parts (a) and (b) for samples of size 10. d. Repeat parts (a) and (b) for samples of size 100.
Transcribed Image Text:**7.81 Household Size** In Example 7.9 on page 322, we conducted a simulation to check the plausibility of the central limit theorem. The variable under consideration is household size, and the population consists of all U.S. households. A frequency distribution for household size of U.S. households is presented in Table 7.7. a. Suppose that you simulate 1000 samples of four households each, determine the sample mean of each of the 1000 samples, and obtain a histogram of the 1000 sample means. Would you expect the histogram to be bell-shaped? Explain your answer. b. Carry out the tasks in part (a) and note the shape of the histogram. c. Repeat parts (a) and (b) for samples of size 10. d. Repeat parts (a) and (b) for samples of size 100.
**Table 7.7: Frequency Distribution for U.S. Household Size** This table represents the frequency distribution of different household sizes in the United States, measured in millions. It is structured into two columns: - **Number of People**: This column lists the possible number of people in a household, ranging from 1 to 7. - **Frequency (millions)**: This column shows how many millions of households there are for each corresponding household size. Here is the data distribution: - Households with 1 person: 31.4 million - Households with 2 people: 39.5 million - Households with 3 people: 18.6 million - Households with 4 people: 16.1 million - Households with 5 people: 7.4 million - Households with 6 people: 2.8 million - Households with 7 people: 1.7 million The table provides insight into the prevalence of various household sizes across the U.S., highlighting that 2-person households are the most common, followed by 1-person households.
Transcribed Image Text:**Table 7.7: Frequency Distribution for U.S. Household Size** This table represents the frequency distribution of different household sizes in the United States, measured in millions. It is structured into two columns: - **Number of People**: This column lists the possible number of people in a household, ranging from 1 to 7. - **Frequency (millions)**: This column shows how many millions of households there are for each corresponding household size. Here is the data distribution: - Households with 1 person: 31.4 million - Households with 2 people: 39.5 million - Households with 3 people: 18.6 million - Households with 4 people: 16.1 million - Households with 5 people: 7.4 million - Households with 6 people: 2.8 million - Households with 7 people: 1.7 million The table provides insight into the prevalence of various household sizes across the U.S., highlighting that 2-person households are the most common, followed by 1-person households.
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