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Questions and Answers
Questions and Answers
What do you discover in activity 9-4?
What do you discover in activity 9-4?
The Empirical Rule
A normal distribution has what kind of shape?
A normal distribution has what kind of shape?
- Skewed left
- Bell-shaped (correct)
- Skewed right
- Uniform
What is the formula for calculating the z-score?
What is the formula for calculating the z-score?
z = (x - μ) / σ
Observations above the mean should have ______ z-scores.
Observations above the mean should have ______ z-scores.
Using the empirical rule, what percentage of the data falls within 1 standard deviation of the mean?
Using the empirical rule, what percentage of the data falls within 1 standard deviation of the mean?
What is the definition of standardization?
What is the definition of standardization?
What is the definition of the empirical rule?
What is the definition of the empirical rule?
In a normal distribution, what is the name for the 'mean'?
In a normal distribution, what is the name for the 'mean'?
In a normal distribution, what is the name for the 'standard deviation'?
In a normal distribution, what is the name for the 'standard deviation'?
What is the name of the data point that falls within 1 standard deviation above the mean?
What is the name of the data point that falls within 1 standard deviation above the mean?
What is the name of the data point that falls within 2 standard deviations below the mean?
What is the name of the data point that falls within 2 standard deviations below the mean?
What is the formula used to find the z-score for a specific value in a normal distribution?
What is the formula used to find the z-score for a specific value in a normal distribution?
Which plot would be used to determine if sample data plausibly came from a normal distribution?
Which plot would be used to determine if sample data plausibly came from a normal distribution?
What does the CLT stand for?
What does the CLT stand for?
What is the guideline size for a sample size unless a population is extremely non-normal?
What is the guideline size for a sample size unless a population is extremely non-normal?
What are the three sources of variation?
What are the three sources of variation?
How does the spread of the sampling distribution of X compare to the spread of the population distribution?
How does the spread of the sampling distribution of X compare to the spread of the population distribution?
What is the symbol for the population mean?
What is the symbol for the population mean?
What is the symbol for the sample mean?
What is the symbol for the sample mean?
Is the population mean fixed or variable?
Is the population mean fixed or variable?
Is the sample mean fixed or variable?
Is the sample mean fixed or variable?
Is the long-term pattern to this variation predictable?
Is the long-term pattern to this variation predictable?
What other term is given to the "mean of the sample means"?
What other term is given to the "mean of the sample means"?
The sampling distribution of the sample means becomes more and more variable as the sample size increases.
The sampling distribution of the sample means becomes more and more variable as the sample size increases.
What conditions have to be met before you can apply the CLT?
What conditions have to be met before you can apply the CLT?
What is the difference between statistical significance and statistical confidence?
What is the difference between statistical significance and statistical confidence?
What are the two factors that determine the distance between the population parameter and sample statistic?
What are the two factors that determine the distance between the population parameter and sample statistic?
The z-score does not indicate how many standard deviations above or below the mean a particular value falls?
The z-score does not indicate how many standard deviations above or below the mean a particular value falls?
The sample size increases as the sampling distribution of the sample mean looks more and more like a normal distribution.
The sample size increases as the sampling distribution of the sample mean looks more and more like a normal distribution.
Describe the properties of normal curves.
Describe the properties of normal curves.
What is an example of a statistical calculation that can be performed on a normal distribution?
What is an example of a statistical calculation that can be performed on a normal distribution?
Explain how to calculate the probability of a value falling within a specific range in a normal distribution using a calculator.
Explain how to calculate the probability of a value falling within a specific range in a normal distribution using a calculator.
Explain how to assess whether sample data could come from a normally distributed population based on normal probability plots and graphs.
Explain how to assess whether sample data could come from a normally distributed population based on normal probability plots and graphs.
Which of the following would be considered a reasonable estimate for the standard deviation if the range of a set of data is 36 and the data appears mound shaped?
Which of the following would be considered a reasonable estimate for the standard deviation if the range of a set of data is 36 and the data appears mound shaped?
Which of the following scenarios is NOT possible?
Which of the following scenarios is NOT possible?
Match the following graphs of normal distributions with their appropriate mean and standard deviation.
Match the following graphs of normal distributions with their appropriate mean and standard deviation.
A student received a 540 on their SAT, with a mean of 478 and a standard deviation of 92, what is the minimum score they need to raise their score on their second attempt to improve it?
A student received a 540 on their SAT, with a mean of 478 and a standard deviation of 92, what is the minimum score they need to raise their score on their second attempt to improve it?
A symmetrical, mound-shaped distribution has a mean of 42 and a standard deviation of 7. Which of the following is true? (Select one that is correct.)
A symmetrical, mound-shaped distribution has a mean of 42 and a standard deviation of 7. Which of the following is true? (Select one that is correct.)
In general, which vary more: averages or individual observations?
In general, which vary more: averages or individual observations?
Give an intuitive explanation for your answer to the previous question.
Give an intuitive explanation for your answer to the previous question.
Which vary more: averages based on a few observations or averages based on many observations?
Which vary more: averages based on a few observations or averages based on many observations?
Suppose the IQ scores of students at a certain college follow a normal distribution with a mean of 115 and a standard deviation of 12. Draw a well-labeled sketch of this distribution
Suppose the IQ scores of students at a certain college follow a normal distribution with a mean of 115 and a standard deviation of 12. Draw a well-labeled sketch of this distribution
Shade in the area corresponding to the proportion of students with an IQ less than 100. Based on this shaded region, make an educated guess as to this proportion of students.
Shade in the area corresponding to the proportion of students with an IQ less than 100. Based on this shaded region, make an educated guess as to this proportion of students.
Use the normal model to determine the proportion of students with an IQ score less than 100.
Use the normal model to determine the proportion of students with an IQ score less than 100.
Determine the proportion of undergraduates having IQs between 110 and 130.
Determine the proportion of undergraduates having IQs between 110 and 130.
Determine how high a student's IQ must be to be in the top 1% of all IQs at this college.
Determine how high a student's IQ must be to be in the top 1% of all IQs at this college.
Find the z* values that cut off the top 5%, top 2.5%, top 1%, and top 0.5% of a standard normal distribution.
Find the z* values that cut off the top 5%, top 2.5%, top 1%, and top 0.5% of a standard normal distribution.
Questions and Answers
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Flashcards
Flashcards
Empirical Rule
Empirical Rule
For mound-shaped, symmetric distributions, approximately 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three.
Z-score
Z-score
A standardized score indicating how many standard deviations a value is above or below the mean.
What is Standardization?
What is Standardization?
Converting a value to a standard score, or z-score, so you can compare values from different distributions.
What are the properties of a Normal Distribution?
What are the properties of a Normal Distribution?
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How does a Normal Probability Plot help?
How does a Normal Probability Plot help?
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Sampling Distribution
Sampling Distribution
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What affects the sampling distribution of the sample mean?
What affects the sampling distribution of the sample mean?
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Central Limit Theorem for Sample Means (CLT)
Central Limit Theorem for Sample Means (CLT)
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What are the conditions for using the CLT for Sample Means?
What are the conditions for using the CLT for Sample Means?
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What is a parameter?
What is a parameter?
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What is a statistic?
What is a statistic?
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Statistical Significance
Statistical Significance
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What is the p-value?
What is the p-value?
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Statistical Confidence
Statistical Confidence
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What are the factors that determine statistical confidence?
What are the factors that determine statistical confidence?
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What is invNorm( on a calculator used for?
What is invNorm( on a calculator used for?
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What is the purpose of a Confidence Interval?
What is the purpose of a Confidence Interval?
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How is the width of a confidence interval affected?
How is the width of a confidence interval affected?
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What is the difference between a population distribution and a sampling distribution?
What is the difference between a population distribution and a sampling distribution?
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What is a normal probability plot used for?
What is a normal probability plot used for?
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What is a normal distribution?
What is a normal distribution?
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What is the relationship between the central limit theorem and statistical inference?
What is the relationship between the central limit theorem and statistical inference?
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Why is it important to check the conditions for using the CLT?
Why is it important to check the conditions for using the CLT?
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What is the difference between 'less than' and 'at least' when calculating probabilities?
What is the difference between 'less than' and 'at least' when calculating probabilities?
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Why is the sampling distribution of x-bar important for statistical inference?
Why is the sampling distribution of x-bar important for statistical inference?
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What is the standard deviation of the sampling distribution called?
What is the standard deviation of the sampling distribution called?
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What is a p-value used for in hypothesis testing?
What is a p-value used for in hypothesis testing?
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What is the difference between a one-tailed and a two-tailed hypothesis test?
What is the difference between a one-tailed and a two-tailed hypothesis test?
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What is a confidence level?
What is a confidence level?
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What is the relationship between confidence level and the width of a confidence interval?
What is the relationship between confidence level and the width of a confidence interval?
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What are the potential sources of variation between sample statistics and population parameters?
What are the potential sources of variation between sample statistics and population parameters?
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Study Notes
Study Notes
Unit 4 Study Guide: Randomness in Data: Normal and Sampling Distributions
- Topics Covered: Topics 9, 12, 14, and 15
- Key Concepts: Randomness in data, normal distributions, sampling distributions
- Check Your Understanding: All material in the Study Guide should be completed for each topic. Check answers using the provided key on Schoology. Ask questions in class or during extra review. Use Google Doc practice problems for extra practice and solutions are available on Google Doc and in the Study Guide
- Review: Complete the Review Sheet at the end of the unit; answers are at the end of the problems in the Study Guide.
- Unit 4 Test: Scheduled for Dec 12/13
- Study Resources: Check Schoology for topic specific keys and extra practice problems in the Google Doc.
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