AQA A-Level Further Mathematics Further statistics overview quiz quiz

$\operatorname{Var}(X) = E(X^2) - [E(X)]^2$

$\operatorname{Var}(X) = E(X) - [E(X)]^2$

$\operatorname{Var}(X) = [E(X)]^2 - E(X^2)$

$\operatorname{Var}(X) = E(X^2) - E(X)$

$15$

$45$

$17$

$47$

The mean is twice the variance

The variance is the square of the mean

The mean and variance are both equal to $\lambda$

The mean is $\lambda$ and the variance is $\sqrt{\lambda}$

$0$

$3e^{-3}$

$1 - e^{-3}$

$e^{-3}$

$\text{Po}(8)$

$\text{Po}(4)$

$\text{Po}(12)$

$\text{Po}(3)$

When $n$ is small and $p$ is large, taking $\lambda = n(1 - p)$ as the rate

When $n$ is large and $p$ is small, using $\lambda = np$

When $p = 0.5$, so that the binomial is perfectly symmetric about its mean

When $n = p$, so that the two parameters of the binomial are numerically equal

$Z = \frac{\bar{x} - \mu}{\sigma}$, dividing by the population standard deviation

$Z = \frac{\bar{x} - \mu}{\sigma / n}$, dividing by the variance over the sample size

$Z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$

$Z = \frac{\mu - \bar{x}}{\sigma^2 / \sqrt{n}}$, using the variance in the denominator

Failing to reject a null hypothesis that is false

Choosing the wrong test statistic

Using a two-tailed test instead of one-tailed

Rejecting a null hypothesis that is actually true

$\chi^2 = \sum \frac{(O - E)^2}{E}$

$\chi^2 = \sum \frac{O - E}{E}$

$\chi^2 = \sum \frac{(O - E)^2}{O}$

$\chi^2 = \sum (O - E)^2$

$12$

$7$

$6$

$5$

$\bar{x} \pm 1.96\sigma$

$\bar{x} \pm 1.96\frac{\sigma}{\sqrt{n}}$

$\bar{x} \pm 1.96\frac{\sigma}{n}$

$\bar{x} \pm 2.576\frac{\sigma}{\sqrt{n}}$

It becomes narrower because the critical value gets smaller as confidence rises

It stays exactly the same width since the critical value does not depend on confidence

It shifts along the axis but keeps the same width as the original interval

It becomes wider because the critical value increases