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What does the parameter 'σ' represent in statistical terms?
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σ (sigma) represents the standard deviation of a numerical variable.
What is the main distinction between nominal and ordinal categorical data?
Nominal data has no intrinsic order, while ordinal data has some kind of order.
What is represented by the symbol μ in statistics?
The mean of a numerical variable, also known as the population mean.
What does it mean if a data distribution is skewed?
A skewed distribution has a long tail on one side; it is asymmetric, with more values on one side than the other.
What does the parameter θ signify in the context of statistical estimation?
θ represents the true, long-term value or parameter that we are trying to estimate.
What are the real-world implications of p-hacking in scientific research?
P-hacking leads to invalid conclusions and misleading results, undermining the credibility of scientific research.
What type of statistical distribution is characterized by two peaks?
Bi-modal distribution.
Why is it important to avoid the terms 'prove' or 'accept' when discussing hypothesis testing results?
Because hypothesis testing cannot definitively prove or accept a hypothesis; it can only provide evidence to reject or fail to reject the null hypothesis.
Describe how a larger sample size impacts the sampling distribution.
Larger sample sizes reduce variance, thereby decreasing the likelihood of extreme sample means.
How does discrete numerical data differ from continuous numerical data?
Discrete data contains finite values, whereas continuous data can be subdivided infinitely.
What is the common threshold for the level of significance in hypothesis testing and what does it mean?
The common level of significance is 5%, meaning if the p-value is less than 0.05, we reject the null hypothesis.
How does p-value help in making decisions during hypothesis testing?
The p-value measures how extreme the sample data is under the null hypothesis; a low p-value indicates that the null hypothesis is unlikely, leading to its rejection.
What is a 'null hypothesis' in the context of hypothesis testing?
The null hypothesis is an initial assumption or statement that there is no effect or no difference, tested against the alternative hypothesis.
Define what a 'confidence interval' represents in statistical data analysis.
A confidence interval quantifies the uncertainty in our estimate of a population parameter, providing a range where the true parameter value is likely to fall.
Explain the concept of a probability density function (PDF).
A PDF describes the probability distribution of a continuous random variable, depicting the likelihood of various outcomes.
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