Podcast
Questions and Answers
What is the primary purpose of a one-tailed test?
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 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?
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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?
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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?
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What is the symbol for the population standard deviation?
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What is the central limit theorem (CLT) about?
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What is the null hypothesis?
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When do you reject the null hypothesis?
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What is the purpose of the significance level (alpha) in hypothesis testing?
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What is the rejection region in hypothesis testing?
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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).
