The 2006 Statistical Abstract of the United States reports on a survey that asked a national sample of 80,000 American households about pet ownership. Suppose (for now) that one-third of all American households own a pet cat.Is this number (one-third) a parameter or a statistic? Explain. What symbol is used to represent the number?What does the Central Limit Theorem say about how the sample proportion of households who own a pet cat could vary under repeated random sampling? Comment on shape, center, and spread of the distribution. Also draw a well-labeled sketch of this sampling distribution.Still supposing that one-third of all American households own a pet cat, between what two values do you expect 95% of all sample proportions to fall?Explain why the interval in part (3) turns out to be so narrow.This survey found that 31.6% of the households sampled owned a pet cat. Is this number a parameter or a statistic? Explain. What symbol is used to represent the value?Indicate this sample proportion (.316) on your sketch of the sampling distribution in part (2), and calculate its z-score.Use the CLT to approximate the probability of obtaining a sample proportion as far from one-third as the one obtained in this sample.Do the sample data provide evidence that the population proportion of households who own a pet cat is not one-third? Explain.

Answered: 2006 Statistical Abstract of the United…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.4: Collecting Data

Problem 3E

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The 2006 Statistical Abstract of the United States reports on a survey that asked a national sample of 80,000 American households about pet ownership. Suppose (for now) that one-third of all American households own a pet cat.

Is this number (one-third) a parameter or a statistic? Explain. What symbol is used to represent the number?
What does the Central Limit Theorem say about how the sample proportion of households who own a pet cat could vary under repeated random sampling? Comment on shape, center, and spread of the distribution. Also draw a well-labeled sketch of this sampling distribution.
Still supposing that one-third of all American households own a pet cat, between what two values do you expect 95% of all sample proportions to fall?
Explain why the interval in part (3) turns out to be so narrow.
This survey found that 31.6% of the households sampled owned a pet cat. Is this number a parameter or a statistic? Explain. What symbol is used to represent the value?
Indicate this sample proportion (.316) on your sketch of the sampling distribution in part (2), and calculate its z-score.
Use the CLT to approximate the probability of obtaining a sample proportion as far from one-third as the one obtained in this sample.
Do the sample data provide evidence that the population proportion of households who own a pet cat is not one-third? Explain.

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