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

$0.25$

$0.5$

$0.75$

$1$

$0.16$

$0.34$

$0.50$

$0.84$

$0.6 \pm 0.05$

$0.6 \pm 0.15$

$0.6 \pm 0.20$

$0.6 \pm 0.10$

$0.7$

$0.49$

$0.61$

$1.1$

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

$P(A) + P(B)$

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

$P(A) - P(B)$

$\frac{1}{2}$

$\frac{1}{3}$

$1$

$\frac{2}{3}$

$0.16$

$0.34$

$0.50$

$0.84$

$0.3$

$0.000225$

$0.015$

$0.0015$

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

$0.4 \cdot 10$

$0.4^4$

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

Define $\hat{p} = \frac{x}{n}$ from the sample and state $z \approx 1.96$ for 95 percent. Substitute into $\hat{p} \pm z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$, give the interval to the required accuracy, then interpret it in context.

I will work out the sample proportion, decide for myself roughly how far either side of it the true value probably lies, and then write down an interval that looks sensible, without using any formula, quantile or statement of what the interval means.

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

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