Questions and Answers
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?
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?
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.
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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?
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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.
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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.
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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?
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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?
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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.
