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If the population proportion is p = 0.60, will the shape of the sampling distribution of \hat{p} predicted for random samples of size 100 be approximately Normal?
If the population proportion is p = 0.60, will the shape of the sampling distribution of \hat{p} predicted for random samples of size 100 be approximately Normal?
True
What is the symbol for population proportion and what is the symbol for sample proportion?
What is the symbol for population proportion and what is the symbol for sample proportion?
p is the symbol for population proportion and p̂ is the symbol for sample proportion.
What is the numerical value of the statistic \hat{p} that estimates p?
What is the numerical value of the statistic \hat{p} that estimates p?
The numerical value of \hat{p} is 755 / 1100.
As sample size increases, the standard deviation of the sampling distribution of \hat{p} also increases.
As sample size increases, the standard deviation of the sampling distribution of \hat{p} also increases.
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What is the probability that a random sample of 200 Utahns will have 22% or more that are obese, given a reported 20% obesity rate?
What is the probability that a random sample of 200 Utahns will have 22% or more that are obese, given a reported 20% obesity rate?
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For samples of size 200, sampling distributions for \hat{p} are more bell shaped when p is close to 0.5 than when p is close to zero or one.
For samples of size 200, sampling distributions for \hat{p} are more bell shaped when p is close to 0.5 than when p is close to zero or one.
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How do the shapes of the sampling distributions for the proportion of voters favoring Initiative 1 and Amendment 3 compare?
How do the shapes of the sampling distributions for the proportion of voters favoring Initiative 1 and Amendment 3 compare?
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Margin of error gives us an idea of how far our point estimate might be from the parameter it estimates.
Margin of error gives us an idea of how far our point estimate might be from the parameter it estimates.
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What is the correct interpretation for the 95% large sample confidence interval (0.089, 0.111)?
What is the correct interpretation for the 95% large sample confidence interval (0.089, 0.111)?
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What is the symbol for 'the hypothesized value for p' when testing H0: p = p0?
What is the symbol for 'the hypothesized value for p' when testing H0: p = p0?
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What could researchers do to decrease the required sample size for estimating the proportion of primary-care physicians who participate in doctor-assisted suicide?
What could researchers do to decrease the required sample size for estimating the proportion of primary-care physicians who participate in doctor-assisted suicide?
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What parameter do we estimate in order to compare the proportions from two populations?
What parameter do we estimate in order to compare the proportions from two populations?
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Study Notes
Sampling Distribution of Sample Proportion
- For a population proportion ( p = 0.60 ), the sampling distribution of ( \hat{p} ) for a sample size of 100 is approximately Normal since both ( np ) and ( n(1-p) ) exceed 10.
- The sampling distribution for ( \hat{p} ) is closer to Normal when ( p ) is around 0.5 than when it is near 0 or 1.
Symbols in Statistics
- Population proportion is denoted as ( p ).
- Sample proportion is represented as ( \hat{p} ).
Estimating Proportions
- To estimate ( p ), use ( \hat{p} = \frac{755}{1100} ).
- Null hypothesis parameter for testing is indicated by ( p_0 ).
Standard Deviation and Sample Size
- Standard deviation of the sampling distribution of ( \hat{p} ) decreases as sample size ( n ) increases, contrary to the notion that it increases.
Probability Calculations
- To calculate the probability of observing at least 22% obesity in a sample of 200 Utahns, compute the z-score and find the corresponding area under the standard Normal curve.
- The calculated z-score of 0.71 provides a right-tail probability of 0.2389.
Confidence Intervals
- A 95% confidence interval for the proportion of adults who cannot identify their country on a map is (0.089, 0.111), indicating strong confidence in the estimate range.
- Margin of error reflects how much the point estimate might deviate from the actual population parameter.
Sample Size Considerations
- To reduce sample size in estimating proportions, decrease the required confidence level, which can lower study costs while maintaining usability of results.
Comparing Proportions
- The difference between two population proportions, ( p_1 - p_2 ), is estimated to compare two different populations effectively.
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Description
Test your knowledge of Statistics concepts with our Stats 121 final flashcards. This quiz covers key topics including sampling distribution and population proportions, providing you with a quick review to prepare for your exam.
