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 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 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

In a PMCC hypothesis test, what do you conclude if \(|r|\) is larger than the critical value?
  1. Reject the null hypothesis
  2. Accept the null hypothesis as true
  3. Use a one-tailed test instead
  4. Set the sample correlation to zero

Question 8

In a test for zero population correlation, what is the null hypothesis?
  1. \(H_0:\rho=0\)
  2. \(H_0:r=0\)
  3. \(H_0:\rho\ne0\)
  4. \(\rho\ne0\)

Question 9

What does a small p-value usually suggest in a hypothesis test?
  1. Evidence against \(H_0\)
  2. Evidence for \(H_0\)
  3. A larger sample is impossible
  4. The test must be two-tailed

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

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

What does independence mean for events \(A\) and \(B\)?
  1. Knowing \(B\) occurred does not change the probability of \(A\).
  2. \(A\) and \(B\) cannot both occur.
  3. \(A\) and \(B\) have equal probabilities.
  4. \(A\) must cause \(B\).

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. A boundary between the rejection and non-rejection regions
  2. The observed value of every data item
  3. The probability that \(H_0\) is true
  4. The mean of the sample

Question 23

What is a normal distribution?
  1. A continuous symmetric bell-shaped distribution
  2. A discrete distribution with two outcomes
  3. A distribution where all values are equally likely
  4. A skewed distribution with no mean

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 \(H_0\) is true
  2. Failing to reject \(H_0\) when \(H_0\) is false
  3. Using a two-tailed test instead of a one-tailed test
  4. Choosing a sample that is too large

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 \(Z\sim N(0,1)\), what is \(P(Z<0)\)?
  1. \(0.5\)
  2. \(0\)
  3. \(0.95\)
  4. \(1\)

Question 29

Why is a continuity correction used when approximating a binomial distribution by a normal distribution?
  1. It adjusts discrete boundaries for a continuous model.
  2. It changes the mean from \(np\) to \(p\).
  3. It removes the need to know \(n\).
  4. It makes dependent trials independent.

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

Why is a normal variable standardised?
  1. To convert it to a standard normal variable for probability calculations
  2. To make its variance equal to \(0\)
  3. To remove all outliers
  4. To turn it into a binomial variable

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 number of independent trials with two outcomes and constant success probability
  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

In a regression context, what is the response variable?
  1. The variable being predicted or explained
  2. The variable used to make the prediction
  3. The sample size
  4. The correlation coefficient

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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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