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central limit theorem
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In random sampling with a large sample size – where n=30 is usually sufficient – the sampling distribution of the sample mean \(\bar{y}\) will be approximately normally distributed, irrespective of the shape of the population distribution
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confidence interval
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A confidence interval constructs an interval of numbers which will contain the true parameter of the population (e.g. the mean) in \((1-\alpha)\) times of cases. \(\alpha\) is usually chosen to be small, so that our confidence interval has a probability of 95% or 99%.
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confidence level
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The confidence level is the probability with which the confidence interval is believed to contain the true parameter of the population and is defined as \((1-\alpha)\)
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degrees of freedom
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Degrees of freedom express constraints on our estimation process by specifying how many values in the calculation are free to vary
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significance level
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The significance level, denoted by \(\alpha\), is the threshold used in hypothesis testing to determine if a result is statistically significant. It represents the probability of rejecting the null hypothesis when it’s actually true (a Type I error). Common levels are 0.05 or 0.01, indicating 5% or 1% risk. We will cover this properly in Week 9.
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t-distribution
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The t-Distribution is bell-shaped and symmetrical around a mean of zero. Its shape is dependent on the degrees of freedom in the estimation process.
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