Statistics (AS) questions

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Statistics (AS) question collection

Review Statistics (AS) questions for Maths, with correct answers shown and coverage across using sampling terminology; summarising data; working with probability distributions.

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Question 1

For an upper one-tailed test of a binomial proportion, which alternative hypothesis is used?
  1. \(H_1: p > p_0\)
  2. \(H_1: p < p_0\)
  3. \(H_1: p = p_0\)
  4. \(H_1: p \ne p_0\)

Question 2

For a two-tailed test of a binomial proportion, which alternative hypothesis is used?
  1. \(H_1: p \ne p_0\)
  2. \(H_1: p > p_0\)
  3. \(H_1: p < p_0\)
  4. \(H_1: p = p_0\)

Question 3

If events \(A\) and \(B\) are independent, what is \(P(A\cap B)\)?
  1. \(P(A)P(B)\)
  2. \(P(A)+P(B)\)
  3. \(P(A)+P(B)-P(A\cap B)\)
  4. \(0\)

Question 4

If events \(A\) and \(B\) are mutually exclusive, what is \(P(A\cap B)\)?
  1. \(0\)
  2. \(1\)
  3. \(P(A)P(B)\)
  4. \(P(A)+P(B)\)

Question 5

If a product moment correlation coefficient is close to \(-1\), what does it suggest?
  1. Strong negative linear correlation
  2. Strong positive linear correlation
  3. Little or no linear correlation
  4. A causal relationship

Question 6

A PMCC is close to \(1\). Which description fits?
  1. Strong positive linear correlation
  2. Strong negative association
  3. Weak positive association
  4. Little linear association

Question 7

For \(X\sim B(n,p)\), what is \(\operatorname{Var}(X)\)?
  1. \(np(1-p)\)
  2. \(np\)
  3. \(n(1-p)\)
  4. \(p(1-p)\)

Question 8

For \(X\sim B(n,p)\), what is \(E(X)\)?
  1. \(np\)
  2. \(p\)
  3. \(n(1-p)\)
  4. \(np(1-p)\)

Question 9

A test statistic lies in the critical region. What conclusion follows?
  1. Reject \(H_0\)
  2. Retain \(H_0\)
  3. Reject \(H_1\)
  4. Increase the sample size

Question 10

In a hypothesis test, which hypothesis is tested directly?
  1. The null hypothesis, \(H_0\)
  2. The alternative hypothesis, \(H_1\)
  3. The sampling frame
  4. The critical value

Question 11

What does a \(5\%\) significance level mean?
  1. A 5% risk of wrongly rejecting the null hypothesis
  2. A 5% chance that the alternative hypothesis is true
  3. A sample containing 5% of the population
  4. A test statistic within 5% of the mean

Question 12

Which formula gives \(P(A\cup B)\)?
  1. \(P(A)+P(B)-P(A\cap B)\)
  2. \(P(A)P(B)\)
  3. \(P(A)+P(B)+P(A\cap B)\)
  4. \(P(A\cap B)\)

Question 13

Which formula gives the probability of the complement of event \(A\), written \(A'\)?
  1. \(P(A')=1-P(A)\)
  2. \(P(A')=P(A)-1\)
  3. \(P(A')=P(A)\)
  4. \(P(A')=1+P(A)\)

Question 14

A full list is numbered and a random number generator selects \(50\) people. Which sampling method is this?
  1. Simple random sampling
  2. Systematic sampling
  3. Quota sampling
  4. Opportunity sampling

Question 15

A researcher samples people who are easiest to access at the time. Which sampling method is this?
  1. Opportunity sampling
  2. Stratified sampling
  3. Simple random sampling
  4. Systematic sampling

Question 16

A sample is taken from each age group in proportion to the population. Which sampling method is this?
  1. Stratified sampling
  2. Quota sampling
  3. Opportunity sampling
  4. Systematic sampling

Question 17

After a random start, every \(10\)th name on a list is chosen. Which sampling method is this?
  1. Systematic sampling
  2. Simple random sampling
  3. Quota sampling
  4. Opportunity sampling

Question 18

A survey needs fixed numbers from several age groups, and the interviewer chooses people non-randomly. Which sampling method is this?
  1. Quota sampling
  2. Stratified random sampling
  3. Simple random sampling
  4. Systematic sampling

Question 19

For \(X\sim B(10,0.4)\), which expression gives \(P(X=3)\)?
  1. \(\binom{10}{3}(0.4)^3(0.6)^7\)
  2. \(\binom{10}{3}(0.4)^7(0.6)^3\)
  3. \(\binom{10}{4}(0.4)^3(0.6)^7\)
  4. \((0.4)^3(0.6)^7\)

Question 20

Which formula gives \(P(A\mid B)\)?
  1. \(\frac{P(A\cap B)}{P(B)}\)
  2. \(\frac{P(A\cap B)}{P(A)}\)
  3. \(P(A)P(B)\)
  4. \(\frac{P(A\cup B)}{P(B)}\)

Question 21

If \(X\) is discrete, which event is equivalent to \(X>3\)?
  1. \(X\ge4\)
  2. \(X\ge3\)
  3. \(X>2\)
  4. \(X\le3\)

Question 22

If \(X\) is discrete, which expression is equivalent to \(P(X>3)\)?
  1. \(1-P(X\le3)\)
  2. \(1-P(X\le4)\)
  3. \(1-P(X\le2)\)
  4. \(1-P(X<3)\)

Question 23

If \(X\) is discrete, which event is equivalent to \(X<5\)?
  1. \(X\le4\)
  2. \(X\le5\)
  3. \(X<4\)
  4. \(X\ge5\)

Question 24

What does the standard deviation measure?
  1. The spread of data values around the mean
  2. The middle value of ordered data
  3. The most common data value
  4. The direction of correlation

Question 25

Which graph is used to estimate the median from grouped cumulative data?
  1. Cumulative frequency graph
  2. Scatter diagram
  3. Frequency polygon
  4. Pie chart

Question 26

What is a census?
  1. Data collection from every member of the population
  2. Data collection from a randomly chosen subset
  3. A list used to choose a sample
  4. A sample chosen in fixed proportions

Question 27

What is a critical region in a hypothesis test?
  1. Test-statistic values that reject the null hypothesis
  2. Values that prove the null hypothesis is true
  3. The set of all possible samples
  4. The values removed as outliers

Question 28

What makes a hypothesis test one-tailed?
  1. \(H_1\) specifies one direction
  2. \(H_1\) uses not equal
  3. The critical region is split
  4. \(H_0\) uses a sample estimate

Question 29

What is the population in a statistical investigation?
  1. The full set of items or people of interest
  2. The subset actually observed
  3. The list used to draw a sample
  4. One selected item from the data set

Question 30

What is a regression line used for?
  1. Predicting a response variable
  2. Measuring linear correlation strength
  3. Identifying possible outliers
  4. Estimating cumulative frequency

Question 31

What is a sample?
  1. A subset selected from a population
  2. The full population being studied
  3. A value that is far from the rest
  4. A rule for rejecting \(H_0\)

Question 32

What is a sampling frame?
  1. A list of available population members
  2. The subset selected from the population
  3. The target population for the study
  4. The method used to select members

Question 33

Using the rule \(Q_1-1.5\times IQR\) and \(Q_3+1.5\times IQR\), what is being identified?
  1. Possible outliers
  2. Quartiles
  3. Class boundaries
  4. Regression estimates

Question 34

What is sampling bias?
  1. Systematic over- or under-representation
  2. Random variation between samples
  3. A sample smaller than its population
  4. Variation within the population

Question 35

In a histogram, how is frequency density calculated?
  1. Frequency divided by class width
  2. Class width divided by frequency
  3. Frequency multiplied by class width
  4. Cumulative frequency divided by total frequency

Question 36

What does the product moment correlation coefficient measure?
  1. Strength and direction of a linear relationship
  2. Gradient of a fitted linear relationship
  3. Strength of any non-linear relationship
  4. Difference between the two variable means

Question 37

In a histogram, what does the area of a bar represent?
  1. Frequency
  2. Frequency density
  3. Class width
  4. Cumulative frequency

Question 38

How is the interquartile range calculated?
  1. \(Q_3-Q_1\)
  2. \(Q_1-Q_3\)
  3. \(Q_2-Q_1\)
  4. \(Q_3+Q_1\)

Question 39

For a positively skewed data set, which statement is usually true?
  1. The mean is greater than the median.
  2. The mean is less than the median.
  3. The mean and median must be equal.
  4. The mode must be greater than the mean.

Question 40

Which distribution models the number of successes in \(n\) fixed independent trials with constant success probability?
  1. Binomial distribution
  2. Normal distribution
  3. Discrete uniform distribution
  4. Continuous uniform distribution

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Review Statistics (AS) questions for Maths, with correct answers shown and coverage across using sampling terminology; summarising data; working with probability distributions.

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