What would you use? Ch 9 CI vs Significance Test

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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 true value of an unknown population parameter. It is expressed with a certain level of confidence, such as 95%.

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CCSS.HSS.IC.B.4

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What is the difference between a confidence interval and a significance test?

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A confidence interval estimates the range of values for a population parameter, while a significance test assesses whether there is enough evidence to reject a null hypothesis.

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CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

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What is a 1 Sample t interval?

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A 1 Sample t interval is used to estimate the mean of a population based on a sample when the population standard deviation is unknown and the sample size is small (typically n < 30).

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CCSS.HSS.IC.B.4

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What is a 1 Sample z interval?

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A 1 Sample z interval is used to estimate the mean of a population based on a sample when the population standard deviation is known or the sample size is large (typically n ≥ 30).

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CCSS.HSS.IC.B.4

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What is a 1 Sample z test for proportions?

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A 1 Sample z test for proportions is used to determine if the proportion of a sample is significantly different from a known population proportion.

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What is a 1 Sample t test?

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A 1 Sample t test is used to determine if the mean of a sample is significantly different from a known value when the population standard deviation is unknown.

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What is the purpose of using a significance level (α)?

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The significance level (α) is the threshold for determining whether to reject the null hypothesis. Common values are 0.05, 0.01, and 0.025.

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How do you calculate a confidence interval for a proportion?

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To calculate a confidence interval for a proportion, use the formula: CI = p̂ ± Z * √(p̂(1-p̂)/n), where p̂ is the sample proportion, Z is the z-score for the desired confidence level, and n is the sample size.

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CCSS.HSS.IC.B.4

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What does it mean if a confidence interval does not include the null hypothesis value?

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If a confidence interval does not include the null hypothesis value, it suggests that there is significant evidence to reject the null hypothesis.

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CCSS.HSS.IC.B.4

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What is the Central Limit Theorem?

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The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normally distributed, regardless of the population distribution, as long as the sample size is sufficiently large.