Podcast
Questions and Answers
What is the primary purpose of a one-tailed test?
What is the primary purpose of a one-tailed test?
Which type of error occurs when the null hypothesis is retained despite being false?
Which type of error occurs when the null hypothesis is retained despite being false?
What is the effect of increasing alpha on type I and type II errors?
What is the effect of increasing alpha on type I and type II errors?
What is the purpose of a critical value in hypothesis testing?
What is the purpose of a critical value in hypothesis testing?
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Which statistical test is used to compare the mean of a single sample to a known or hypothesized population mean?
Which statistical test is used to compare the mean of a single sample to a known or hypothesized population mean?
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What is the relationship between type I and type II errors?
What is the relationship between type I and type II errors?
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How can the risk of type I error be minimized?
How can the risk of type I error be minimized?
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What is the primary advantage of a two-tailed test over a one-tailed test?
What is the primary advantage of a two-tailed test over a one-tailed test?
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What is the main goal of inferential statistics?
What is the main goal of inferential statistics?
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What is the symbol for the population standard deviation?
What is the symbol for the population standard deviation?
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What is the central limit theorem (CLT) about?
What is the central limit theorem (CLT) about?
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What is the null hypothesis?
What is the null hypothesis?
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When do you reject the null hypothesis?
When do you reject the null hypothesis?
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What is the purpose of the significance level (alpha) in hypothesis testing?
What is the purpose of the significance level (alpha) in hypothesis testing?
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What is the rejection region in hypothesis testing?
What is the rejection region in hypothesis testing?
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What is the alternative hypothesis?
What is the alternative hypothesis?
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Study Notes
Inferential Statistics
- Used to describe the population based on the observations of the sample
- Deals with making inferences about the population parameters (μ, σ) based on sample statistics (x, s)
Population and Sample Characteristics
- Population characteristics: parameters (μ = mean, σ = standard deviation)
- Sample characteristics: statistics (x = mean, s = standard deviation)
Central Limit Theorem (CLT)
- States that the distribution of sample means will be approximately normally distributed, regardless of the population's original shape, as long as the sample size is large enough
Hypothesis Testing
- Null hypothesis: states that the treatment has no effect, meaning any observed differences are due to random chance
- Alternative hypothesis: the treatment has an effect, indicating that observed differences are due to the treatment
Decision Making in Hypothesis Testing
- Retain the null hypothesis: if observed data are consistent with the null hypothesis, and the results can be reasonably attributed to chance
- Reject the null hypothesis: if the likelihood that the observed results are due to chance is very small, and the results are statistically significant
Significance Level and Alpha
- Significance level (alpha): probability threshold set by the researcher that defines the boundaries for rejecting or retaining the null hypothesis
- Typically set at 0.05
Rejection Region and Critical Value
- Rejection region: area in the tail(s) of the sampling distribution that represents the sample means that are highly unlikely to occur if the null hypothesis is true
- Critical value: threshold or cutoff point on the test statistic distribution that defines the boundaries of the rejection region
One-Tailed and Two-Tailed Tests
- One-tailed test: used when there is a directional alternative, and the rejection region is located entirely in one tail of the probability distribution
- Two-tailed test: used when the alternative hypothesis does not specify a direction of the effect, and tests for the possibility of an effect in both directions
Decision Errors
- Type I error: rejecting the null hypothesis when it is true
- Type II error: retaining the null hypothesis when it is false
- Both types of errors are mutually exclusive, and changes in one type of error have an effect on the other type
Minimizing Type I and Type II Errors
- To minimize type II error: increase alpha, increase N, use the most powerful statistical test, and have a good experimental design
- To minimize type I error: decrease alpha
Single Sample T-Test
- Used to determine whether the mean of a single sample differs significantly from a known or hypothesized population mean
- Used when the standard deviation of a population is unknown and needs to be estimated
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Description
This quiz covers the basics of inferential statistics, including parameters and statistics, and the Central Limit Theorem (CLT).
