Hypothesis Testing and Contingency Tables (AQA A-Level Further Maths): Quizzes

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Confidence Intervals
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Why is the denominator n1n-1 rather than nn in the sample variance formula?

Makes s2s^2 an unbiased estimator of σ2\sigma^2

What does it mean for a statistic to be an unbiased estimator?

Expected value equals population parameter

If a population has variance σ2\sigma^2 and sample size is nn, what is the variance of Xˉ\bar{X}?

σ2n\frac{\sigma^2}{n}

What sample size is considered large enough to use s2s^2 in place of σ2\sigma^2?

At least 30

What is the standard error of the mean when population variance is unknown?

sn\frac{s}{\sqrt{n}}

What is the zz-value for a 95% confidence interval?

1.96

What happens to confidence interval width when confidence level increases?

Width increases

If sample size is multiplied by 4, what happens to the confidence interval width?

Halves

After calculating a 95% CI, how should you interpret it?

We are 95% confident μ\mu lies in interval

When should you use σ\sigma instead of ss in the confidence interval formula?

When population variance is known

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