Probability and statistics (Maths Methods Units 3 and 4) quiz

$p$

$np(1-p)$

$np$

$n - p$

Mutually exclusive

Independent

Both A and B

Neither

$0.25$

$0.5$

$0.75$

$1$

$0.16$

$0.34$

$0.50$

$0.84$

$0.6 \pm 0.05$

$0.6 \pm 0.15$

$0.6 \pm 0.20$

$0.6 \pm 0.10$

$0.7$

$0.49$

$0.61$

$1.1$

$P(A) \cdot P(B)$

$P(A) + P(B)$

$P(A) + P(B) - P(A \cap B)$

$P(A) - P(B)$

A chi-squared goodness-of-fit test that compares observed and expected category counts

A correlation test only, checking the strength of association between two variables

Linear regression, fitting a line of best fit and testing its gradient

A $z$-test for a proportion or mean, comparing sample statistic to hypothesised value

$0.16$

$0.34$

$0.50$

$0.84$

$\sigma$, unchanged by the sample size

$\frac{\sigma}{n}$, dividing by the full sample size

$\frac{\sigma}{\sqrt{n}}$

$n \sigma$, scaling up with the sample size

$\binom{10}{4} \cdot 0.4^6 \cdot 0.6^4$

$0.4 \cdot 10$

$0.4^4$

$\binom{10}{4} \cdot 0.4^4 \cdot 0.6^6$

State the null hypothesis $H_0$ and alternative $H_1$ in terms of the population parameter. Compute the test statistic from the sample. Compare to the critical value (or $p$-value) at the given significance level. Conclude in context.

I will test the claim by working out the sample mean, deciding for myself whether it looks far enough from the claimed value to matter, and then simply stating whether the claim seems true without writing any hypotheses or computing a test statistic.

Statistics is mostly about probability, so I will just describe the chances involved in words.

First, find the mean, and treat that single number as the whole answer to the question.