Questions S3 (621 questions)

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AQA S3 2016 June Q2
15 marks Moderate -0.3
A plane flies regularly between airports D and T with an intermediate stop at airport M. The time of the plane's departure from, or arrival at, each airport is classified as either early, on time, or late. On 90\% of flights, the plane departs from D on time, and on 10\% of flights, it departs from D late. Of those flights that depart from D on time, 65\% then depart from M on time and 35\% depart from M late. Of those flights that depart from D late, 15\% then depart from M on time and 85\% depart from M late. Any flight that departs from M on time has probability 0.25 of arriving at T early, probability 0.60 of arriving at T on time and probability 0.15 of arriving at T late. Any flight that departs from M late has probability 0.10 of arriving at T early, probability 0.20 of arriving at T on time and probability 0.70 of arriving at T late.
  1. Represent this information by a tree diagram on which labels and percentages or probabilities are shown. [3 marks]
  2. Hence, or otherwise, calculate the probability that the plane:
    1. arrives at T on time;
    2. arrives at T on time, given that it departed from D on time;
    3. does not arrive at T late, given that it departed from D on time;
    4. does not arrive at T late, given that it departed from M on time.
    [8 marks]
  3. Three independent flights of the plane depart from D on time. Calculate the probability that two flights arrive at T on time and that one flight arrives at T early. [4 marks]
AQA S3 2016 June Q3
7 marks Standard +0.3
Car parking in a market town's high street was, until 31 May 2014, limited to one hour free of charge between 8 am and 6 pm. Records show that, during a period of 30 days prior to this date, a total of 315 penalty tickets were issued. Car parking in the high street later became limited to thirty minutes free of charge between 8 am and 6 pm. A subsequent investigation revealed that, during a period of 60 days from 1 October 2014, a total of 747 penalty tickets were issued. The daily numbers of penalty tickets issued may be modelled by independent Poisson distributions with means \(\lambda_A\) until 31 May 2014 and \(\lambda_B\) from 1 October 2014. Investigate, at the 1\% level of significance, a claim by traders on the high street that \(\lambda_B > \lambda_A\). [7 marks]
AQA S3 2016 June Q4
13 marks Standard +0.3
Ben is a fencing contractor who is often required to repair a garden fence by replacing a broken post between fence panels, as illustrated. \includegraphics{figure_4} The tasks involved are as follows. \(U\): detach the two fence panels from the broken post \(V\): remove the broken post \(W\): insert a new post \(X\): attach the two fence panels to the new post The mean and the standard deviation of the time, in minutes, for each of these tasks are shown in the table.
TaskMeanStandard deviation
\(U\)155
\(V\)4015
\(W\)7520
\(X\)2010
The random variables \(U\), \(V\), \(W\) and \(X\) are pairwise independent, except for \(V\) and \(W\) for which \(\rho_{VW} = 0.25\).
  1. Determine values for the mean and the variance of:
    1. \(R = U + X\);
    2. \(F = V + W\);
    3. \(T = R + F\);
    4. \(D = W - V\).
    [8 marks]
  2. Assuming that each of \(R\), \(F\), \(T\) and \(D\) is approximately normally distributed, determine the probability that:
    1. the total time taken by Ben to repair a garden fence is less than 3 hours;
    2. the time taken by Ben to insert a new post is at least 1 hour more than the time taken by him to remove the broken post.
    [5 marks]
AQA S3 2016 June Q5
10 marks Standard +0.3
  1. The random variable \(X\), which has distribution \(\mathrm{N}(\mu_X, \sigma^2)\), is independent of the random variable \(Y\), which has distribution \(\mathrm{N}(\mu_Y, \sigma^2)\). In order to test \(\mathrm{H_0}: \mu_X = 1.5\mu_Y\), samples of size \(n\) are taken on each of \(X\) and \(Y\) and the random variable \(D\) is defined as $$D = \overline{X} - 1.5\overline{Y}$$ State the distribution of \(D\) assuming that \(\mathrm{H_0}\) is true. [4 marks]
  2. A machine that fills bags with rice delivers weights that are normally distributed with a standard deviation of 4.5 grams. The machine fills two sizes of bags: large and extra-large. The mean weight of rice in a random sample of 50 large bags is 1509 grams. The mean weight of rice in an independent random sample of 50 extra-large bags is 2261 grams. Test, at the 5\% level of significance, the claim that, on average, the rice in an extra-large bag is \(1\frac{1}{3}\) times as heavy as that in a large bag. [6 marks]
AQA S3 2016 June Q6
22 marks Standard +0.3
  1. The discrete random variable \(X\) has probability distribution given by $$\mathrm{P}(X = x) = \begin{cases} \frac{e^{-\lambda}\lambda^x}{x!} & x = 0, 1, 2, \ldots \\ 0 & \text{otherwise} \end{cases}$$ Show that \(\mathrm{E}(X) = \lambda\) and that \(\mathrm{Var}(X) = \lambda\). [7 marks]
  2. In light-weight chain, faults occur randomly and independently, and at a constant average rate of 0.075 per metre.
    1. Calculate the probability that there are no faults in a 10-metre length of this chain. [2 marks]
    2. Use a distributional approximation to estimate the probability that, in a 500-metre reel of light-weight chain, there are:
      1. fewer than 30 faults;
      2. at least 35 faults but at most 45 faults.
      [7 marks]
  3. As part of an investigation into the quality of a new design of medium-weight chain, a sample of fifty 10-metre lengths was selected. Subsequent analysis revealed a total of 49 faults. Assuming that faults occur randomly and independently, and at a constant average rate, construct an approximate 98\% confidence interval for the average number of faults per metre. [6 marks]
OCR S3 2012 January Q1
6 marks Moderate -0.8
In a test of association of two factors, \(A\) and \(B\), a \(2 \times 2\) contingency table yielded \(5.63\) for the value of \(\chi^2\) with Yates' correction.
  1. State the null hypothesis and alternative hypothesis for the test. [1]
  2. State how Yates' correction is applied, and whether it increases or decreases the value of \(\chi^2\). [2]
  3. Carry out the test at the \(2\frac{1}{2}\%\) significance level. [3]
OCR S3 2012 January Q2
7 marks Standard +0.3
An investigation in 2007 into the incidence of tuberculosis (TB) in badgers in a certain area found that 42 out of a random sample of 190 badgers tested positive for TB. In 2010, 48 out of a random sample of 150 badgers tested positive for TB.
  1. Assuming that the population proportions of badgers with TB are the same in 2007 and 2010, obtain the best estimate of this proportion. [1]
  2. Carry out a test at the \(2\frac{1}{2}\%\) significance level of whether the population proportion of badgers with TB increased from 2007 to 2010. [6]
OCR S3 2012 January Q3
8 marks Standard +0.3
The continuous random variable \(U\) has a normal distribution with unknown mean \(\mu\) and known variance 1. A random sample of four observations of \(U\) gave the values \(3.9, 2.1, 4.6\) and \(1.4\).
  1. Calculate a \(90\%\) confidence interval for \(\mu\). [3]
  2. The probability that the sum of four random observations of \(U\) is less than 11 is denoted by \(p\). For each of the end points of the confidence interval in part (i) calculate the corresponding value of \(p\). [5]
OCR S3 2012 January Q4
10 marks Standard +0.3
\(X\) is a continuous random variable with the distribution N\((48.5, 12.5^2)\). The values of \(X\) are transformed to standardised values of \(Y\), using the equation \(Y = aX + b\), where \(a\) and \(b\) are constants with \(a > 0\).
  1. Find values of \(a\) and \(b\) for which the mean and standard deviation of \(Y\) are 40 and 10 respectively. [4]
  2. State the distribution of \(Y\). [1]
Two randomly chosen standardised values are denoted by \(Y_1\) and \(Y_2\).
  1. Calculate the probability that \(Y_2\) is at least 10 greater than \(Y_1\). [5]
OCR S3 2012 January Q5
10 marks Standard +0.3
A statistician suggested that the weekly sales \(X\) thousand litres at a petrol station could be modelled by the following probability density function. $$\text{f}(x) = \begin{cases} \frac{1}{40}(2x + 3) & 0 \leqslant x < 5, \\ 0 & \text{otherwise.} \end{cases}$$
  1. Show that, using this model, P\((a < X < a + 1) = \frac{a + 2}{20}\) for \(0 \leqslant a < 4\). [3]
Sales in 100 randomly chosen weeks gave the following grouped frequency table.
\(x\)\(0 \leqslant x < 1\)\(1 \leqslant x < 2\)\(2 \leqslant x < 3\)\(3 \leqslant x < 4\)\(4 \leqslant x < 5\)
Frequency1612183024
  1. Carry out a goodness of fit test at the \(10\%\) significance level of whether f\((x)\) fits the data. [7]
OCR S3 2012 January Q6
13 marks Standard +0.3
The continuous random variable \(Y\) has probability density function given by $$\text{f}(y) = \begin{cases} -\frac{1}{4}y & -2 < y < 0, \\ \frac{1}{4}y & 0 \leqslant y \leqslant 2, \\ 0 & \text{otherwise.} \end{cases}$$ Find
  1. the interquartile range of \(Y\), [4]
  2. Var\((Y)\), [5]
  3. E\((|Y|)\). [4]
OCR S3 2012 January Q7
18 marks Standard +0.3
The manufacturer's specification for batteries used in a certain electronic game is that the mean lifetime should be 32 hours. The manufacturer tests a random sample of 10 batteries made in Factory A, and the lifetimes (\(x\) hours) are summarised by \(n = 10\), \(\sum x = 289.0\) and \(\sum x^2 = 8586.19\). It may be assumed that the population of lifetimes has a normal distribution.
  1. Carry out a one-tail test at the \(5\%\) significance level of whether the specification is being met. [7]
  2. Justify the use of a one-tail test in this context. [1]
Batteries made with the same specification are also made in Factory B. The lifetimes of these batteries are also normally distributed. A random sample of 12 batteries from this factory was tested. The lifetimes are summarised by \(n = 12\), \(\sum x = 363.0\) and \(\sum x^2 = 11290.95\).
    1. State what further assumption must be made in order to test whether there is any difference in the mean lifetimes of batteries made at the two factories. Use the data to comment on whether this assumption is reasonable. [3]
    2. Carry out the test at the \(10\%\) significance level. [7]
OCR MEI S3 2006 January Q1
18 marks Standard +0.3
A railway company is investigating operations at a junction where delays often occur. Delays (in minutes) are modelled by the random variable \(T\) with the following cumulative distribution function. $$F(t) = \begin{cases} 0 & t \leq 0 \\ 1 - e^{-\frac{1}{t}} & t > 0 \end{cases}$$
  1. Find the median delay and the 90th percentile delay. [5]
  2. Derive the probability density function of \(T\). Hence use calculus to find the mean delay. [5]
  3. Find the probability that a delay lasts longer than the mean delay. [2]
You are given that the variance of \(T\) is 9.
  1. Let \(\overline{T}\) denote the mean of a random sample of 30 delays. Write down an approximation to the distribution of \(\overline{T}\). [3]
  2. A random sample of 30 delays is found to have mean 4.2 minutes. Does this cast any doubt on the modelling? [3]
OCR MEI S3 2006 January Q2
18 marks Standard +0.3
Geoffrey is a university lecturer. He has to prepare five questions for an examination. He knows by experience that it takes about 3 hours to prepare a question, and he models the time (in minutes) taken to prepare one by the Normally distributed random variable \(X\) with mean 180 and standard deviation 12, independently for all questions.
  1. One morning, Geoffrey has a gap of 2 hours 50 minutes (170 minutes) between other activities. Find the probability that he can prepare a question in this time. [3]
  2. One weekend, Geoffrey can devote 14 hours to preparing the complete examination paper. Find the probability that he can prepare all five questions in this time. [3]
A colleague, Helen, has to check the questions.
  1. She models the time (in minutes) to check a question by the Normally distributed random variable \(Y\) with mean 50 and standard deviation 6, independently for all questions and independently of \(X\). Find the probability that the total time for Geoffrey to prepare a question and Helen to check it exceeds 4 hours. [3]
  2. When working under pressure of deadlines, Helen models the time to check a question in a different way. She uses the Normally distributed random variable \(\frac{1}{2}X\), where \(X\) is as above. Find the length of time, as given by this model, which Helen needs to ensure that, with probability 0.9, she has time to check a question. [4]
Ian, an educational researcher, suggests that a better model for the time taken to prepare a question would be a constant \(k\) representing "thinking time" plus a random variable \(T\) representing the time required to write the question itself, independently for all questions.
  1. Taking \(k\) as 45 and \(T\) as Normally distributed with mean 120 and standard deviation 10 (all units are minutes), find the probability according to Ian's model that a question can be prepared in less than 2 hours 30 minutes. [2]
Juliet, an administrator, proposes that the examination should be reduced in time and shorter questions should be used.
  1. Juliet suggests that Ian's model should be used for the time taken to prepare such shorter questions but with \(k = 30\) and \(T\) replaced by \(\frac{2}{3}T\). Find the probability as given by this model that a question can be prepared in less than \(1\frac{1}{4}\) hours. [3]
OCR MEI S3 2006 January Q3
18 marks Standard +0.3
A production line has two machines, A and B, for delivering liquid soap into bottles. Each machine is set to deliver a nominal amount of 250 ml, but it is not expected that they will work to a high level of accuracy. In particular, it is known that the ambient temperature affects the rate of flow of the liquid and leads to variation in the amounts delivered. The operators think that machine B tends to deliver a somewhat greater amount than machine A, no matter what the ambient temperature. This is being investigated by an experiment. A random sample of 10 results from the experiment is shown below. Each column of data is for a different ambient temperature.
Ambient temperature\(T_1\)\(T_2\)\(T_3\)\(T_4\)\(T_5\)\(T_6\)\(T_7\)\(T_8\)\(T_9\)\(T_{10}\)
Amount delivered by machine A246.2251.6252.0246.6258.4251.0247.5247.1248.1253.4
Amount delivered by machine B248.3252.6252.8247.2258.8250.0247.2247.9249.0254.5
  1. Use an appropriate \(t\) test to examine, at the 5\% level of significance, whether the mean amount delivered by machine B may be taken as being greater than that delivered by machine A, stating carefully your null and alternative hypotheses and the required distributional assumption. [11]
  2. Using the data for machine A in the table above, provide a two-sided 95\% confidence interval for the mean amount delivered by this machine, stating the required distributional assumption. Explain whether you would conclude that the machine appears to be working correctly in terms of the nominal amount as set. [7]
OCR MEI S3 2006 January Q4
18 marks Standard +0.3
Quality control inspectors in a factory are investigating the lengths of glass tubes that will be used to make laboratory equipment.
  1. Data on the observed lengths of a random sample of 200 glass tubes from one batch are available in the form of a frequency distribution as follows.
    Length \(x\) (mm)Observed frequency
    \(x \leq 298\)1
    \(298 < x \leq 300\)30
    \(300 < x \leq 301\)62
    \(301 < x \leq 302\)70
    \(302 < x \leq 304\)34
    \(x > 304\)3
    The sample mean and standard deviation are 301.08 and 1.2655 respectively. The corresponding expected frequencies for the Normal distribution with parameters estimated by the sample statistics are
    Length \(x\) (mm)Expected frequency
    \(x \leq 298\)1.49
    \(298 < x \leq 300\)37.85
    \(300 < x \leq 301\)55.62
    \(301 < x \leq 302\)58.32
    \(302 < x \leq 304\)44.62
    \(x > 304\)2.10
    Examine the goodness of fit of a Normal distribution, using a 5\% significance level. [7]
  2. It is thought that the lengths of tubes in another batch have an underlying distribution similar to that for the batch in part (i) but possibly with different location and dispersion parameters. A random sample of 10 tubes from this batch gives the following lengths (in mm). 301.3 \quad 301.4 \quad 299.6 \quad 302.2 \quad 300.3 \quad 303.2 \quad 302.6 \quad 301.8 \quad 300.9 \quad 300.8
    1. Discuss briefly whether it would be appropriate to use a \(t\) test to examine a hypothesis about the population mean length for this batch. [2]
    2. Use a Wilcoxon test to examine at the 10\% significance level whether the population median length for this batch is 301 mm. [9]
OCR MEI S3 2008 June Q1
19 marks Moderate -0.8
  1. Sarah travels home from work each evening by bus; there is a bus every 20 minutes. The time at which Sarah arrives at the bus stop varies randomly in such a way that the probability density function of \(X\), the length of time in minutes she has to wait for the next bus, is given by $$f(x) = k(20-x) \text{ for } 0 \leq x \leq 20, \text{ where } k \text{ is a constant.}$$
    1. Find \(k\). Sketch the graph of \(f(x)\) and use its shape to explain what can be deduced about how long Sarah has to wait. [5]
    2. Find the cumulative distribution function of \(X\) and hence, or otherwise, find the probability that Sarah has to wait more than 10 minutes for the bus. [4]
    3. Find the median length of time that Sarah has to wait. [3]
    1. Define the term 'simple random sample'. [2]
    2. Explain briefly how to carry out cluster sampling. [3]
    3. A researcher wishes to investigate the attitudes of secondary school pupils to pollution. Explain why he might prefer to collect his data using a cluster sample rather than a simple random sample. [2]
OCR MEI S3 2008 June Q2
18 marks Standard +0.3
An electronics company purchases two types of resistor from a manufacturer. The resistances of the resistors (in ohms) are known to be Normally distributed. Type A have a mean of 100 ohms and standard deviation of 1.9 ohms. Type B have a mean of 50 ohms and standard deviation of 1.3 ohms.
  1. Find the probability that the resistance of a randomly chosen resistor of type A is less than 103 ohms. [3]
  2. Three resistors of type A are chosen at random. Find the probability that their total resistance is more than 306 ohms. [3]
  3. One resistor of type A and one resistor of type B are chosen at random. Find the probability that their total resistance is more than 147 ohms. [3]
  4. Find the probability that the total resistance of two randomly chosen type B resistors is within 3 ohms of one randomly chosen type A resistor. [5]
  5. The manufacturer now offers type C resistors which are specified as having a mean resistance of 300 ohms. The resistances of a random sample of 100 resistors from the first batch supplied have sample mean 302.3 ohms and sample standard deviation 3.7 ohms. Find a 95\% confidence interval for the true mean resistance of the resistors in the batch. Hence explain whether the batch appears to be as specified. [4]
OCR MEI S3 2008 June Q3
18 marks Standard +0.3
  1. A tea grower is testing two types of plant for the weight of tea they produce. A trial is set up in which each type of plant is grown at each of 8 sites. The total weight, in grams, of tea leaves harvested from each plant is measured and shown below.
    SiteABCDEFGH
    Type I225.2268.9303.6244.1230.6202.7242.1247.5
    Type II215.2242.1260.9241.7245.5204.7225.8236.0
    1. The grower intends to perform a \(t\) test to examine whether there is any difference in the mean yield of the two types of plant. State the hypotheses he should use and also any necessary assumption. [3]
    2. Carry out the test using a 5\% significance level. [7]
  2. The tea grower deals with many types of tea and employs tasters to rate them. The tasters do this by giving each tea a score out of 100. The tea grower wishes to compare the scores given by two of the tasters. Their scores for a random selection of 10 teas are as follows.
    TeaQRSTUVWXYZ
    Taster 169798563816585868977
    Taster 274759966756496949686
    Use a Wilcoxon test to examine, at the 5\% level of significance, whether it appears that, on the whole, the scores given to teas by these two tasters differ. [8]
OCR MEI S3 2008 June Q4
17 marks Standard +0.3
  1. A researcher is investigating the feeding habits of bees. She sets up a feeding station some distance from a beehive and, over a long period of time, records the numbers of bees arriving each minute. For a random sample of 100 one-minute intervals she obtains the following results.
    Number of bees01234567\(\geq 8\)
    Number of intervals61619181714640
    1. Show that the sample mean is 3.1 and find the sample variance. Do these values support the possibility of a Poisson model for the number of bees arriving each minute? Explain your answer. [3]
    2. Use the mean in part (i) to carry out a test of the goodness of fit of a Poisson model to the data. [10]
  2. The researcher notes the length of time, in minutes, that each bee spends at the feeding station. The times spent are assumed to be Normally distributed. For a random sample of 10 bees, the mean is found to be 1.465 minutes and the standard deviation is 0.3288 minutes. Find a 95\% confidence interval for the overall mean time. [4]
OCR MEI S3 2010 June Q1
18 marks Moderate -0.8
  1. The manager of a company that employs 250 travelling sales representatives wishes to carry out a detailed analysis of the expenses claimed by the representatives. He has an alphabetical (by surname) list of the representatives. He chooses a sample of representatives by selecting the 10th, 20th, 30th and so on. Name the type of sampling the manager is attempting to use. Describe a weakness in his method of using it, and explain how he might overcome this weakness. [3]
The representatives each use their own cars to drive to meetings with customers. The total distance, in miles, travelled by a representative in a month is Normally distributed with mean 2018 and standard deviation 96.
  1. Find the probability that, in a randomly chosen month, a randomly chosen representative travels more than 2100 miles. [3]
  2. Find the probability that, in a randomly chosen 3-month period, a randomly chosen representative travels less than 6000 miles. What assumption is needed here? Give a reason why it may not be realistic. [5]
  3. Each month every representative submits a claim for travelling expenses plus commission. Travelling expenses are paid at the rate of 45 pence per mile. The commission is 10\% of the value of sales in that month. The value, in £, of the monthly sales has the distribution N(21200, 1100²). Find the probability that a randomly chosen claim lies between £3000 and £3300. [7]
OCR MEI S3 2010 June Q2
18 marks Standard +0.3
William Sealy, a biochemistry student, is doing work experience at a brewery. One of his tasks is to monitor the specific gravity of the brewing mixture during the brewing process. For one particular recipe, an initial specific gravity of 1.040 is required. A random sample of 9 measurements of the specific gravity at the start of the process gave the following results. 1.046 \quad 1.048 \quad 1.039 \quad 1.055 \quad 1.038 \quad 1.054 \quad 1.038 \quad 1.051 \quad 1.038
  1. William has to test whether the specific gravity of the mixture meets the requirement. Why might a \(t\) test be used for these data and what assumption must be made? [3]
  2. Carry out the test using a significance level of 10\%. [9]
  3. Find a 95\% confidence interval for the true mean specific gravity of the mixture and explain what is meant by a 95\% confidence interval. [6]
OCR MEI S3 2010 June Q3
18 marks Standard +0.3
  1. In order to prevent and/or control the spread of infectious diseases, the Government has various vaccination programmes. One such programme requires people to receive a booster injection at the age of 18. It is felt that the proportion of people receiving this booster could be increased and a publicity campaign is undertaken for this purpose. In order to assess the effectiveness of this campaign, health authorities across the country are asked to report the percentage of 18-year-olds receiving the booster before and after the campaign. The results for a randomly chosen sample of 9 authorities are as follows.
    AuthorityABCDEFGHI
    Before769888818684839380
    After829793778395919589
    This sample is to be tested to see whether the campaign appears to have been successful in raising the percentage receiving the booster.
    1. Explain why the use of paired data is appropriate in this context. [1]
    2. Carry out an appropriate Wilcoxon signed rank test using these data, at the 5\% significance level. [10]
  2. Benford's Law predicts the following probability distribution for the first significant digit in some large data sets.
    Digit123456789
    Probability0.3010.1760.1250.0970.0790.0670.0580.0510.046
    On one particular day, the first significant digits of the stock market prices of the shares of a random sample of 200 companies gave the following results.
    Digit123456789
    Frequency55342716151712159
    Test at the 10\% level of significance whether Benford's Law provides a reasonable model in the context of share prices. [7]
OCR MEI S3 2010 June Q4
18 marks Moderate -0.3
A random variable \(X\) has an exponential distribution with probability density function \(f(x) = \lambda e^{-\lambda x}\) for \(x \geq 0\), where \(\lambda\) is a positive constant.
  1. Verify that \(\int_0^{\infty} f(x) \, dx = 1\) and sketch \(f(x)\). [5]
  2. In this part of the question you may use the following result. $$\int_0^{\infty} x^r e^{-\lambda x} \, dx = \frac{r!}{\lambda^{r+1}} \text{ for } r = 0, 1, 2, \ldots$$ Derive the mean and variance of \(X\) in terms of \(\lambda\). [6]
The random variable \(X\) is used to model the lifetime, in years, of a particular type of domestic appliance. The manufacturer of the appliance states that, based on past experience, the mean lifetime is 6 years.
  1. Let \(\overline{X}\) denote the mean lifetime, in years, of a random sample of 50 appliances. Write down an approximate distribution for \(\overline{X}\). [4]
  2. A random sample of 50 appliances is found to have a mean lifetime of 7.8 years. Does this cast any doubt on the model? [3]
Edexcel S3 Q1
6 marks Easy -1.8
  1. Explain briefly the method of quota sampling. [3]
  2. Give one disadvantage of quota sampling compared with stratified sampling. [1]
  3. Describe a situation in which you would choose to use quota sampling rather than stratified sampling and explain why. [2]