Statistics (A2) questions

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Statistics (A2) question collection

Review Statistics (A2) questions for Maths, with correct answers shown and coverage across using conditional probability; working with statistical distributions; interpreting regression and correlation.

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Question 1

When \(X\sim B(n,p)\) is approximated by a normal variable \(Y\), which correction matches \(P(X\ge k)\)?
  1. \(P(Y>k-0.5)\)
  2. \(P(Y>k+0.5)\)
  3. \(P(Y<k-0.5)\)
  4. \(P(Y<k+0.5)\)

Question 2

When \(X\sim B(n,p)\) is approximated by a normal variable \(Y\), which correction matches \(P(X\le k)\)?
  1. \(P(Y<k+0.5)\)
  2. \(P(Y<k-0.5)\)
  3. \(P(Y>k+0.5)\)
  4. \(P(Y>k-0.5)\)

Question 3

When \(X\sim B(n,p)\) is approximated by \(Y\), which correction matches \(P(X<k)\)?
  1. \(P(Y<k-0.5)\)
  2. \(P(Y<k+0.5)\)
  3. \(P(Y>k-0.5)\)
  4. \(P(Y>k+0.5)\)

Question 4

For a model \(y=ax^n\), which plot should be approximately linear?
  1. \(\log y\) against \(\log x\)
  2. \(\log y\) against \(x\)
  3. \(y\) against \(\log x\)
  4. \(x\) against \(y\)

Question 5

If \(Z\sim N(0,1)\), what is \(\operatorname{Var}(Z)\)?
  1. \(1\)
  2. \(0\)
  3. \(\sigma\)
  4. \(\sigma^2\)

Question 6

If \(Z\sim N(0,1)\), what is the mean of \(Z\)?
  1. \(0\)
  2. \(1\)
  3. \(\mu\)
  4. \(\sigma\)

Question 7

A PMCC test uses \(H_1:\rho<0\). If \(r\) is below the negative critical value, what is the conclusion?
  1. Significant negative correlation
  2. Significant positive correlation
  3. No significant correlation
  4. Perfect negative correlation

Question 8

Which null hypothesis tests for zero population correlation?
  1. \(H_0:\rho=0\)
  2. \(H_0:r=0\)
  3. \(H_0:\rho>0\)
  4. \(H_0:\rho<0\)

Question 9

What does a small p-value suggest?
  1. Strong evidence against \(H_0\)
  2. Strong evidence for \(H_0\)
  3. Weak evidence against \(H_0\)
  4. Evidence of sampling bias

Question 10

Which formula gives \(P(A\cap B)\) using \(P(A\mid B)\)?
  1. \(P(B)P(A\mid B)\)
  2. \(P(A)+P(A\mid B)\)
  3. \(P(A)+P(B)\)
  4. \(\dfrac{P(A\mid B)}{P(B)}\)

Question 11

Which formula gives \(P(A\mid B)\)?
  1. \(\dfrac{P(A\cap B)}{P(B)}\)
  2. \(\dfrac{P(A\cap B)}{P(A)}\)
  3. \(P(A)P(B)\)
  4. \(P(A)+P(B)-P(A\cap B)\)

Question 12

For \(X\sim N(\mu,\sigma^2)\), what is \(P(X<\mu)\)?
  1. \(0.5\)
  2. \(0\)
  3. \(0.95\)
  4. \(\sigma\)

Question 13

Which expression standardises \(X\sim N(\mu,\sigma^2)\)?
  1. \(Z=\dfrac{X-\mu}{\sigma}\)
  2. \(Z=\dfrac{X-\mu}{\sigma^2}\)
  3. \(Z=\dfrac{X+\mu}{\sigma}\)
  4. \(Z=\dfrac{\mu-X}{\sigma^2}\)

Question 14

For normal \(X\), approximately what is \(P(\mu-\sigma<X<\mu+\sigma)\)?
  1. \(0.68\)
  2. \(0.50\)
  3. \(0.95\)
  4. \(0.997\)

Question 15

If \(Y\) is the normal approximation to \(X\sim B(n,p)\), what are the mean and variance of \(Y\)?
  1. \(np\text{ and }np(1-p)\)
  2. \(np\text{ and }np\)
  3. \(n\text{ and }p\)
  4. \(np(1-p)\text{ and }np\)

Question 16

Which hypothesis pair is used for a two-tailed test of zero population correlation?
  1. \(H_0:\rho=0,\ H_1:\rho\ne0\)
  2. \(H_0:r=0,\ H_1:r\ne0\)
  3. \(H_0:\rho=0,\ H_1:\rho>0\)
  4. \(H_0:p=0,\ H_1:p\ne0\)

Question 17

Which statement is correct if events \(A\) and \(B\) are independent?
  1. \(P(A\mid B)=P(A)\)
  2. \(P(A\mid B)=P(B)\)
  3. \(P(A\cap B)=0\)
  4. \(P(A\cup B)=1\)

Question 18

For a \(5\%\) two-tailed test, what probability is placed in each tail?
  1. \(0.025\)
  2. \(0.05\)
  3. \(0.10\)
  4. \(0.95\)

Question 19

Events \(A\) and \(B\) are independent, with \(P(A)=0.4\) and \(P(B)=0.5\). Find \(P(A\mid B)\).
  1. \(0.4\)
  2. \(0.2\)
  3. \(0.5\)
  4. \(0.9\)

Question 20

In a PMCC hypothesis test, what does \(\rho\) represent?
  1. The population correlation coefficient
  2. The sample correlation coefficient
  3. The significance level
  4. The regression gradient

Question 21

What does the sample value \(r\) represent in correlation?
  1. The sample correlation coefficient
  2. The population correlation coefficient
  3. The probability of rejection
  4. The residual for one data point

Question 22

What is a critical value in a hypothesis test?
  1. The boundary of the rejection region
  2. The observed value of every data item
  3. The probability that \(H_0\) is true
  4. The mean of the sample

Question 23

Which description fits a normal distribution?
  1. Continuous, symmetric and bell-shaped
  2. Discrete, symmetric and bell-shaped
  3. Continuous, right-skewed and unbounded
  4. Continuous, uniform and bounded

Question 24

If a p-value is less than the significance level, what conclusion is made?
  1. Reject \(H_0\)
  2. Fail to reject \(H_0\)
  3. Increase the p-value
  4. Change to a two-tailed test

Question 25

For \(X\sim N(\mu,\sigma^2)\), where are the points of inflection on the normal curve?
  1. \(\mu-\sigma\) and \(\mu+\sigma\)
  2. \(\mu-\sigma^2\) and \(\mu+\sigma^2\)
  3. \(\mu\) and \(\sigma\)
  4. \(0\) and \(1\)

Question 26

What is a Type I error?
  1. Rejecting \(H_0\) when it is true
  2. Not rejecting \(H_0\) when it is false
  3. Rejecting \(H_0\) when it is false
  4. Not rejecting \(H_0\) when it is true

Question 27

Which model has the form \(y=ab^x\)?
  1. Exponential model
  2. Power model
  3. Linear model
  4. Normal model

Question 28

For \(Z\sim N(0,1)\), approximately what is \(P(-1.96<Z<1.96)\)?
  1. \(0.95\)
  2. \(0.90\)
  3. \(0.975\)
  4. \(0.05\)

Question 29

What does a continuity correction adjust?
  1. Binomial boundaries
  2. The binomial mean
  3. The trial count
  4. Trial independence

Question 30

What range of values can the product moment correlation coefficient take?
  1. \(-1\le r\le 1\)
  2. \(0\le r\le 1\)
  3. \(-\infty<r<\infty\)
  4. \(r\ge 1\)

Question 31

Standardising \(X\sim N(\mu,\sigma^2)\) gives a variable with which distribution?
  1. \(N(0,1)\)
  2. \(N(1,0)\)
  3. \(N(\mu,\sigma)\)
  4. \(B(n,p)\)

Question 32

If \(X\sim N(\mu,\sigma^2)\), what distribution does the sample mean \(\bar X\) have for samples of size \(n\)?
  1. \(\bar X\sim N\left(\mu,\dfrac{\sigma^2}{n}\right)\)
  2. \(\bar X\sim N(\mu,n\sigma^2)\)
  3. \(\bar X\sim N(n\mu,\sigma^2)\)
  4. \(\bar X\sim N(0,1)\)

Question 33

In a normal mean test with known \(\sigma\), which test statistic is used?
  1. \(Z=\dfrac{\bar X-\mu_0}{\sigma/\sqrt n}\)
  2. \(Z=\dfrac{\bar X-\mu_0}{\sigma^2}\)
  3. \(Z=\dfrac{X-\bar X}{\sqrt n}\)
  4. \(Z=\dfrac{\mu_0-\sigma}{\bar X}\)

Question 34

A test is checking whether a population mean has increased from \(\mu_0\). Which alternative hypothesis is used?
  1. \(H_1:\mu>\mu_0\)
  2. \(H_1:\mu<\mu_0\)
  3. \(H_1:\mu=\mu_0\)
  4. \(H_1:\mu\ne\mu_0\)

Question 35

For \(X\sim N(\mu,\sigma^2)\), what is the median?
  1. \(\mu\)
  2. \(\sigma\)
  3. \(\sigma^2\)
  4. \(0\)

Question 36

In a PMCC hypothesis test, which parameter should appear in the hypotheses?
  1. \(\rho\)
  2. \(r\)
  3. \(p\)
  4. \(\bar x\)

Question 37

When is a binomial model usually suitable?
  1. Fixed independent trials, two outcomes, constant \(p\)
  2. Continuous measurements with a symmetric bell shape
  3. A sample mean from a normal population
  4. Bivariate data with a curved trend

Question 38

When is a normal model usually a reasonable choice?
  1. For continuous data that are roughly symmetric and bell-shaped
  2. For fixed trials with only success or failure
  3. For categorical data with no natural order
  4. For data that must be integers from \(0\) to \(n\)

Question 39

For \(X\sim N(50,16)\), what is the standard deviation of \(X\)?
  1. \(4\)
  2. \(16\)
  3. \(50\)
  4. \(\sqrt{50}\)

Question 40

Which regression quantity is the variable being predicted?
  1. Response variable
  2. Explanatory variable
  3. Residual
  4. Fitted value

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Review Statistics (A2) questions for Maths, with correct answers shown and coverage across using conditional probability; working with statistical distributions; interpreting regression and correlation.

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