1.
Explain the difference between a population and a sample, and between a parameter and a statistic. [3]
JD SCIENCE
Statistics
Answer all questions. Show working. Answers are in a separate file on the Worksheets page — do not look at them until you have finished.
2.
Describe simple random sampling and one advantage and one disadvantage. [3]
3.
Describe stratified sampling and when it is better than simple random sampling. [3]
4.
Describe opportunity/convenience sampling and why it can be biased. [2]
5.
A data set has values 2, 5, 7, 10, 16. Find the mean and the standard deviation (divisor n or n−1 as used on your board). [4]
6.
Coded data: y = (x − 20)/2. The mean of y is 3 and the sd of y is 1.4. Find the mean and sd of x. [3]
7.
Interpret a positive skew and a negative skew. Which average is pulled the most? [3]
8.
Two events A and B: P(A)=0.4, P(B)=0.5, P(A∩B)=0.2. Find P(A∪B) and P(A|B). [3]
9.
State the conditions for a binomial distribution B(n, p). [3]
10.
X ~ B(10, 0.3). Find P(X = 2). Leave your answer in a calculable form and evaluate to 3 s.f. [3]
11.
X ~ B(10, 0.3). Find E(X) and Var(X). [2]
12.
X ~ B(20, 0.4). Use your calculator to find P(X ≤ 5). [2]
13.
When can a normal distribution be used as a model? Mention symmetry and the mean/median. [2]
14.
X ~ N(50, 16). Find P(X < 46). Standardise and use Φ. [3]
15.
X ~ N(100, 25). Find the value a such that P(X < a) = 0.975. [3]
16.
State the mean and variance of the standard normal Z. [2]
17.
A hypothesis test: H₀: p = 0.5, H₁: p > 0.5, n = 20, observed 14 successes, 5% level. Carry out the test using a binomial model. [5]
18.
Explain what a Type I error and a Type II error are. [3]
19.
Why do we use a continuity correction when approximating a discrete distribution by a normal? [2]
20.
PMCC: a scatter graph of revision hours and mark has r = 0.82. Interpret r. [2]
21.
The least-squares regression line is y = 12 + 4.5x. Interpret the gradient and the intercept in context if x is hours and y is mark. [3]
22.
Why should you not use a regression line to predict far outside the data range? [2]
23.
A discrete random variable X has P(X=1)=0.2, P(X=2)=0.5, P(X=3)=0.3. Find E(X) and Var(X). [4]
24.
For that X, find P(X ≥ 2). [1]
25.
Describe a histogram versus a box plot: what can you see on each? [3]
26.
Large data set style: a sample of 40 daily maxima has mean 18.2°C. Explain why this mean might not estimate the yearly mean temperature well. [2]
27.
Write H₀ and H₁ for a two-tailed test that a coin is fair, and state the meaning of the significance level. [3]
28.
Y ~ N(0, 1). Find P(−1.96 < Y < 1.96). [2]
29.
On AQA Statistics, you must conclude in context. Write a model concluding sentence for a non-significant result about a plant fertiliser. [2]
30.
The IQR is 12 and the range is 40. Comment on the presence of possible outliers compared with a data set with IQR 12 and range 16. [2]
31.
Explain mutually exclusive vs independent, with a probability condition for each. [3]
32.
A Venn diagram: 50 students, 30 do maths, 22 do physics, 12 do both. A student is chosen at random. Find P(physics | maths). [3]