Confidence Intervals, Sample Size, Hypothesis Test & Linear Regr

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What is a confidence interval?

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A confidence interval is a range of values, derived from a data set, that is likely to contain the value of an unknown population parameter. It is associated with a confidence level that quantifies the level of confidence that the parameter lies within the interval.

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What is the purpose of using a t-distribution instead of a z-distribution?

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The t-distribution is used instead of a z-distribution when the sample size is small (typically n < 30) and the population standard deviation is unknown.

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What is the formula for calculating the sample size needed for estimating a mean?

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What does a p-value represent in hypothesis testing?

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A p-value represents the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true.

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What is the null hypothesis (H0)?

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The null hypothesis (H0) is a statement that there is no effect or no difference, and it serves as the default or starting assumption in hypothesis testing.

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What is the alternative hypothesis (H1)?

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The alternative hypothesis (H1) is a statement that indicates the presence of an effect or a difference, opposing the null hypothesis.

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What is the significance level (alpha) in hypothesis testing?

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The significance level (alpha) is the threshold for determining whether to reject the null hypothesis, commonly set at 0.05.

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What is the relationship between sample size and confidence interval width?

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As the sample size increases, the width of the confidence interval decreases, leading to a more precise estimate of the population parameter.

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What is a one-sample t-test?

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A one-sample t-test is a statistical test used to determine whether the mean of a single sample is significantly different from a known or hypothesized population mean.

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What is the effect of increasing the confidence level on the confidence interval?

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Increasing the confidence level results in a wider confidence interval, as it requires a larger range to ensure that the population parameter is captured.