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A shop records the number of sales it makes each hour over a period of time. Some of the results are shown in the stem-and-leaf graph below.
Key: 5 | 7 = 57 sales
(a)Work out the following statistics for the data above.
| Statistic | Value |
|---|---|
| n, the number of observations | 20 |
| Median | |
| Range | |
| Interquartile range |
(a) working
A company makes mobile phones.
(a)The company carries out a survey on a random sample of n of their customers, where n ∈ ℕ. Based on this survey, the margin of error for the population proportion, 1√n, is 3·4%, correct to 1 decimal place. Find one possible value of n.
(a)
(b)The company makes two types of mobile phones: an old model and a new model. A random sample of 80 of the company’s new mobile phones is tested, to see how long it takes to charge them from empty to fully charged. The mean time for this sample is 45·4 minutes, with a standard deviation of 3·1 minutes.
(i)Use this information to find a 95% confidence interval for the population mean time. Give each value in your answer in minutes, correct to 1 decimal place.
(b)(i)
(ii)The mean time taken to charge the old model mobile phone from empty to fully charged is 44 minutes. The company says that the mean time taken to charge the new model mobile phone is the same as this. Using your answer to part (b)(i), or otherwise, carry out a hypothesis test at the 5% level of significance to test the company’s claim. The null hypothesis is given. State clearly the alternative hypothesis, your conclusion, and the reason for your conclusion. If necessary, provide calculations. [Null hypothesis: The mean time taken to fully charge the new model mobile phone is 44 minutes.]
(b)(ii)
(c)In a different survey, two hypothesis tests were carried out at the 5% level of significance. The p-value for the first test was 0·046. The p-value for the second test was 0·0002. Write a sentence to explain what the difference in the sizes of these p-values means about the conclusions to these two tests. You do not need to carry out any calculations.
(c)
This question is about solar panels. The graph below shows the energy produced each day by a number of solar panels, depending on the number of daylight hours. The axes do not meet at (0, 0). The energy produced is measured in kWh.
Plot the point P and draw your line of best fit directly on the graph
(a)Which of the following is closest to the value of r, the correlation coefficient, for this data? Justify your answer, based on the information in the graph.
Options: −0·95, −0·80, −0·25, 0·25, 0·80, 0·95.
Options: −0·95, −0·80, −0·25, 0·25, 0·80, 0·95.
(a)
(b)According to the line of best fit, a day with 13 daylight hours corresponds to 10·7 kWh of energy being produced.
(i)Plot a point on the graph above to represent this information. Label this point P.
(ii)Draw the line of best fit, by eye, on the graph above. Your line of best fit should go through the point P.
(iii)Use the line of best fit that you have drawn to estimate the amount of energy that would be produced for a day with 11 daylight hours. Show your work on the graph.
(iv)Find the equation of the line of best fit that you drew in part (b)(ii). Use the point P you plotted and your answer from part (b)(iii). Give your answer in the form y = ax + b, where x ∈ ℝ is the number of daylight hours, y is the energy produced (in kWh), and a and b are constants.
(b) working
The amount of money spent on entertainment per month by the adult population in a particular city is roughly normally distributed, with a mean of €46·02 and a standard deviation of €11·72.
(i)Work out the percentage of the adult population who spend more than €50 on entertainment per month. Give your answer correct to the nearest percent.
(a)(i)
(ii)90% of the adult population spend less than €X on entertainment per month. Work out the value of X, correct to the nearest whole number.
(a)(ii)
(a)The ages of twelve people in a class are given below. They are in ascending order, and x ∈ ℕ.
| 11 | 12 | 12 | 14 | 15 | x | 18 | 18 | 19 | 22 | 25 | 30 |
(i)The median age is 17·5. Find the value of x.
(a)(i)
(ii)The first quartile (Q1) is 13. Work out the interquartile range of the ages.
(a)(ii)
(b)Michael finds the mean and the median of a list of 10 numbers. He then changes the biggest number in the list to make it even bigger. Will this change the mean, the median, or both? Justify your answer fully. (Tick one: the mean only / the median only / both the mean and the median.)
(b) — choice & justification
(c)The frequency table below shows the ages of the people in another class, where k ∈ ℕ.
| Age (years) | 24–30 | 30–36 | 36–42 | 42–48 | 48–54 | 54–60 |
|---|---|---|---|---|---|---|
| Number of people | 4 | 5 | 9 | k | 4 | 2 |
Note: 24–30 means “at least 24, and less than 30”, and so on. Using mid-interval values, the mean age of the people in the class is 40·4 years, based on the data in the table above. Use this to work out the value of k.
(c)
A particular test is used to measure how well students around the world can do maths problems.
(a)Worldwide, scores on this test are normally distributed with a mean score of 400 and a standard deviation of 60.
(i)The scaled diagram below shows the distribution of scores on this test. Use the empirical rule to fill in the four missing values in the diagram.
(a)(i) — write the four missing values in the boxes
(ii)Use the normal distribution to work out the proportion of students worldwide who would score above 420 on the test. Give your answer correct to 2 decimal places.
(a)(ii)
A random sample of students is taken from each country that takes part in the maths test. The table below shows the mean score and the standard deviation for this sample from three of these countries, labelled X, Y, and Z. It also shows the size of each of these samples.
| Country | Mean score | Standard deviation | Size of sample |
|---|---|---|---|
| X | 387 | 66·2 | 2161 |
| Y | 403 | 70·6 | 2724 |
| Z | 396 | 53·7 | 2520 |
For parts (b) and (c), use the relevant standard deviation from the table above.
(b)Using values from the table, construct a 95% confidence interval for the population mean score of country X. Give each value correct to 1 decimal place.
(b)
(c)For country Y, researchers carried out a hypothesis test at the 5% level of significance to see if the population mean score of the country was different to 400 (the worldwide mean). The null hypothesis was that the mean score for country Y was 400. The alternative hypothesis was that it was not 400.
(i)Using values from the table, work out the test statistic (z-score) of the sample mean for country Y for this test. Give your answer correct to 2 decimal places.
(c)(i)
(ii)Hence, work out the p-value of this test statistic and state the conclusion of the hypothesis test in the given context, making reference to the mean score for country Y.
(c)(ii)
(d)In country Z, 50% of all students have a pet in their home and 50% do not. Describe how the sample of 2520 students from country Z could be taken as a stratified random sample with respect to having a pet in the home, and explain why it is probably not useful to do this when looking at these students’ maths scores.
(d)
(e)For one of the questions on the test, students are given a mark of 0, 1, 2, or 3. The proportion of students who get each mark is shown in the table below. Here, p, r ∈ ℝ and p, r ≥ 0.
| Mark | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| Proportion | 0·19 | p | 2r | r |
A student is picked at random. The expected value of their mark for this question will depend on the values of p and r. Find the largest value that the expected value of their mark could be.
(e)
A group of 22 students was tested to see how far, in metres, each of them could swim without stopping for a rest. The results are shown in the ordered stem-and-leaf plot below. Four of the entries have been replaced with the letters a, b, c, and d.
Key: 2 | 7 = 27 metres
(a)(i)The mode of the data is 34 metres. Use this to write down the value of a.
(a)(i)
(ii)The range of the data is 49 metres. Use this to find the value of b and the value of c.
(a)(ii)
(iii)The median of the data is 43·5 metres. Use this to find the value of d.
(a)(iii)
Seven of the 22 students took swimming lessons. They were re-tested after the lessons, to see how far they could now swim without stopping. The table and graph below show the results of the initial test and of the re-test for these students.
| Initial (m) | Re-test (m) |
|---|---|
| 22 | 25 |
| 34 | 40 |
| 38 | 65 |
| 45 | 96 |
| 49 | 142 |
| 57 | 262 |
| 61 | 350 |
(b)How would you best describe how the results changed for these students, from the initial test to the re-test?
(b)
(c)The swimming coach worked out r, the correlation coefficient between the distance in the initial test and the distance in the re-test, for these seven students. Find the value of r, correct to 4 decimal places.
(c)
PK Hotels is a hotel chain in Europe.
(a)The ages of the people who stayed in a PK Hotel in 2023 are roughly normally distributed, with a mean age of 48·2 years and a standard deviation of 10·6 years.
(i)One person is picked at random from the people who stayed in a PK Hotel in 2023. Find the probability that this person is less than 50 years old.
(a)(i)
(ii)Exactly 10% of people who stayed in a PK Hotel in 2023 are at least A years old. Find the value of A, correct to the nearest whole number.
(a)(ii)
(d)In 2020, PK Hotels were rated the best hotel chain in Europe by 75% of their customers. In 2024, PK Hotels carried out a survey of a random sample of 1000 of their customers to see if this percentage had changed. Of these, 765 rated PK Hotels the best hotel chain in Europe. Carry out a hypothesis test at the 5% level of significance to see if this shows a change in the percentage of their customers who rate PK Hotels the best chain in Europe. State your null hypothesis and your alternative hypothesis, state your conclusion, and give a reason for your conclusion.
(d)
Rohan has a large number of small cubes, identical in size. Some are red, some green, and the rest blue. Rohan picks out 5 different cubes at random, records the number of each colour, and replaces them. He repeats this a number of times. The table shows the number of cubes of each colour the first 7 times (Trial A to Trial G).
| Trial | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| Red | 0 | 3 | 2 | 2 | 4 | 5 | 1 |
| Green | 4 | 2 | 0 | 3 | 0 | 0 | 2 |
| Blue | 1 | 0 | 3 | 0 | 1 | 0 | 2 |
(i)Work out the mean and standard deviation of the number of red cubes per trial, for these 7 trials. Give each answer correct to 1 decimal place.
(a)(i)
(ii)Work out the correlation coefficient between the number of red cubes and the number of green cubes per trial, for these 7 trials. Give your answer correct to 3 decimal places.
(a)(ii)
(iii)Rohan repeats this experiment a large number of times. Explain why you would expect the correlation coefficient between the number of red cubes and the number of green cubes per trial to be negative.
(a)(iii)
An online word game involves trying to guess a five-letter word in as few attempts as possible. Each player is given a score s (s ∈ ℝ) based on how many attempts it takes them to guess the word.
(a)In Ireland, players' scores are approximately normally distributed, with a mean of 3·87 and a standard deviation of 0·36. A player is selected at random from the players in Ireland. Find the probability that this player has a score of less than 3·5.
(a)
(b)A random sample of 64 Galway players has a mean score of 3·74. Based on this, a local newspaper claims that Galway players have a different mean score to players in Ireland.
(i)Use the information about this sample to construct a 95% confidence interval for the mean score of all Galway players. Use the standard deviation of 0·36 in your calculations.
(b)(i)
(ii)Carry out a hypothesis test at the 5% level of significance to test the newspaper's claim that Galway players have a different mean score to players in Ireland. State your null hypothesis, state your alternative hypothesis, state your conclusion, and give a reason for your conclusion.
(b)(ii)
(c)A national newspaper conducts a survey on a random sample of n teenagers in Ireland. 35% of the sample said they play the online word game every day. Based on this, a 95% confidence interval for the percentage, p, of all teenagers in Ireland who play the game every day was calculated, as accurately as possible. Correct to one decimal place, this interval was 26·5% ≤ p ≤ 43·5%. Use this to work out the value of n, the number of teenagers surveyed.
(c)
(a)A survey on remote learning was carried out on a random sample of 400 students. 135 of the students preferred remote learning over in-person learning. (Give all solutions as decimals, correct to 4 decimal places.)
(i)Work out the proportion of the sample that preferred remote learning.
(a)(i)
(ii)Use the margin of error (1√n) to create a 95% confidence interval for the proportion of the population that preferred remote learning.
(a)(ii)
(iii)Using the proportion from part (a)(i), create a 95% confidence interval for this population proportion that is more accurate than the one based on the margin of error.
(a)(iii)
(b)In 2019, people with a pre-pay mobile phone plan spent an average (mean) of €20·79 on their phone each month. In 2021 a survey of a random sample of 500 pre-pay users gave a mean of €22·16 and a standard deviation of €8·12. Carry out a hypothesis test at the 5% level of significance to see if this shows a change in the mean monthly spend. State your null hypothesis and alternative hypothesis, state your conclusion, and give a reason for your conclusion.
(b)
(a)Jena is researching fuel consumption. She finds the miles per gallon (m/g) for eight cars, A to H, in the city and on the motorway:
| Car | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| City | 22 | 27 | 24 | 16 | 15 | 21 | 30 | 17 |
| Motorway | 34 | 38 | 34 | 27 | 24 | 30 | 40 | 30 |
(i)The scatterplot shows the data for cars A to F. Using the table, plot and label points to represent cars G and H.
(a)(i)
(ii)On the scatterplot, draw the line of best fit for the data, by eye.
(a)(ii)
(iii)Two other cars, K and L, have K: City = 20, and L: Motorway = 60. Use your line of best fit to estimate each missing value. Show your work on the scatterplot.
(a)(iii)
(iv)Based on the data given, would you be more confident in the value you estimated for K or for L? Give a reason for your answer.
(a)(iv)
(v)Find the value of r, the correlation coefficient between city and motorway miles per gallon. Use only the values for the 8 cars A to H. Give your answer correct to 3 decimal places.
(a)(v)
(b)The scatterplot shows some values of fuel consumption (F) for given engine speeds (S), for a particular car. F can be closely approximated by a quadratic function of S. rFS is the correlation coefficient between F and S. Give a reason why you might think that rFS is very close to 0.
(b)
(c)13 customers rated a garage with a whole-number score out of 100. The mean was 52. The median was 54. No two scores were the same. The table shows the 13 scores (in no particular order): Stephen gave S and Mary gave M, where S, M ∈ ℕ. Find the least value and the greatest value that S could be.
| 46 | 68 | 24 | 74 | 42 | 30 | 61 | 54 | 28 | 50 | 57 | S | M |
(c)
(a)In a school all First Years sat a common maths exam. The results (integer values) were normally distributed with a mean of 176 marks and a standard deviation of 36 marks. The top 10% of students go forward to a county competition.
(i)Find the minimum mark needed on the exam to progress to the county stage.
(a)(i)
(ii)The school awarded a Certificate of Merit to any student who achieved between 165 marks and 210 marks. Find the percentage of First Years who received the Certificate of Merit.
(a)(ii)
(b)A news report claimed that 6th year students in Ireland studied an average of 21 hours per week outside class. A survey of 60 randomly chosen 6th year students found an average study time of 19·8 hours and a standard deviation of 5·2 hours.
(i)Find the test statistic (the z-score) of this sample mean.
(b)(i)
(ii)Find the p-value of this test statistic. Comment on what can be concluded in a two-tailed hypothesis test at the 5% level of significance, in relation to the news report claim.
(b)(ii)
(a)An airline company Trans-sky Airways has designed an aptitude test for people applying for jobs as trainee pilots. The aptitude test is scored out of 500 marks. The results are normally distributed with a mean score of 280 and a standard deviation of 90.
(i)The top 25% of people taking the aptitude test are invited back for an interview. Find the minimum mark needed on the test in order to be invited back for interview.
(a)(i)
(ii)Anyone who scores above the 40th percentile can re-sit the test later. Eileen scored 260 marks in the test. Find out whether or not Eileen is eligible to re-sit the test.
(a)(ii)
(b)
(i)Explain the relevance of the z-scores −1·96 and 1·96 in the standard normal distribution.
(b)(i)
(ii)Trans-sky Airways surveyed 2500 of its passengers about a new service it proposed to introduce. The variable p̂ is the proportion of respondents in the survey who said they would use the new service. The radius of the 95% confidence interval of the survey was 0·01568. Find the value of p̂, where 0·5 < p̂ ≤ 1.
(b)(ii)
(c)The weight of the airline passengers' carry-on luggage is normally distributed with a mean of 12 kg. The airline has recently introduced a fee for non-carry-on luggage. After the fee was introduced, the airline expected the mean weight of the carry-on luggage to change. They selected a random sample of 80 passengers and weighed their carry-on luggage. The sample mean was 13·1 kg and the sample standard deviation was 4·5 kg. Test the hypothesis, at the 5% level of significance, that the mean weight of the carry-on luggage has changed. State the null hypothesis and the alternative hypothesis. Give your conclusion in the context of the question.
(c)
(d)The company bus can carry passengers up to a total maximum weight allowance of 3000 kg. The weight of passengers is normally distributed with a mean of 73 kg and a standard deviation of 12 kg. 40 passengers board the bus. Find the probability that the total passenger weight will be over the maximum weight allowance. Give your answer as a percentage correct to 2 decimal places.
(d)
(e)A list consists of eight whole numbers, labelled from A to H. The numbers are all greater than zero and are ordered from smallest to largest. The difference between any two adjacent numbers is 2 or more. The median of the list is 12·5. The lower quartile (the median of the 4 lowest numbers) is 7·5. The interquartile range is 12. The second largest number (G) is 23. The range of the list is 21. The mean of the list is 13·5. Find the numbers which satisfy all of the above conditions.
(e)
A motoring magazine collected data on cars on a particular stretch of road. Certain details on 800 cars were recorded.
(a)(i)The ages of the 800 cars were recorded. 174 of them were new (less than 1 year old). Find the 95% confidence interval for the proportion of new cars on this road. Give your answer correct to 4 significant figures.
(a)(i)
(ii)The data on the speeds of these 800 vehicles is normally distributed with an average speed of 87·3 km/h and a standard deviation of 12 km/h. What proportion of cars on this stretch of road would you expect to find travelling at over 95 km/h?
(a)(ii)
(iii)The driver of a car was told that 70% of all the speeds recorded were higher than his speed. Find the speed at which this driver was recorded. Give your answer correct to the nearest whole number.
(a)(iii)
(b)(i)A road safety programme was carried out in the area. After the programme the motoring magazine recorded the speeds of 100 passing cars and carried out a hypothesis test, at the 5% level of significance, to determine whether the average speed had changed. The p-value of the test was 0·024. What can the magazine conclude based on this p-value? Give a reason for your answer.
(b)(i)
(ii)The magazine found that the average speed of this sample was lower than the previously established average speed of 87·3 km/h. Find the average speed of the cars in this sample, correct to 1 decimal place.
(b)(ii)
(a)The diagram shows the standard normal curve. The shaded area represents 67% of the data. Find the value of z1.
(a)
(b)Maths results had a mean of 70 with a standard deviation of 15. English results (same class) had a mean of 72 with a standard deviation of 10. Both were normally distributed.
(i)Mary got 65 in Maths and 68 in English. In which exam did Mary do better relative to the other students in the class? Justify your answer (using z-scores).
(b)(i)
(ii)In English the top 15% of students were awarded an A grade. Find the least whole number mark that merited the award of an A grade in English.
(b)(ii)
(iii)Using the empirical rule, or otherwise, estimate the percentage of students in the class who scored between 52 and 82 in the English test.
(b)(iii)
Acme Confectionery makes cakes and chocolate bars.
(a)(i)The weights of the new Chocolate Crunch bars are normally distributed with a mean of 4·64 g and a standard deviation of 0·12 g. A sample of 10 bars is selected at random and the mean weight of the sample is found. Find the probability that the mean weight of the sample is between 4·6 g and 4·7 g (sampling distribution).
(a)(i)
(ii)A company surveyed 400 people who had bought at least one bar; 324 said they liked the new bar. Create the 95% confidence interval for the population proportion who liked the new bar. Give your answer correct to 2 decimal places.
(a)(ii)
(b)(i)For each statement, indicate whether it is Always True, Sometimes True or Never True (n = sample size, p̂ = sample proportion): (1) an increased confidence level implies a wider interval; (2) as p̂ increases the estimated standard error increases; (3) as p̂(1 − p̂) increases the estimated standard error increases; (4) as n increases the estimated standard error increases.
(b)(i)
(ii)Using calculus or otherwise, find the maximum value of p̂(1 − p̂).
(b)(ii)
(iii)Hence, find the largest possible value of the radius of the 95% confidence interval for a population proportion, given a random sample of size 800.
(b)(iii)
(c)Acme Confectionery has an employee pension plan. It will pay €20 000 on the day of retirement, then a sum on the same date each year for the next 25 years. Each year the sum paid is 1% more than the previous year. What sum must the company set aside on the day of retirement to fund this pension? Assume an AER of 2·4% (present value of a geometric series).
(c)
An experiment measures the fuel consumption at various speeds for a model of car. Speed (km/h): 40, 48, 56, 64, 88, 96, 112. Fuel consumption (km/litre): 21, 16, 18, 16, 13, 11, 9.
(a)Find the correlation coefficient of the data, correct to 3 decimal places.
(a)
(b)Plot the points on the grid and draw the line of best fit (by eye).
(b)
(c)The slope of the line of best fit is found to be −0·15. What does this value represent in the context of the data?
(c)
(d)Mary drove Cork to Dublin at an average speed of 96 km/h; Jane drove the same journey at 112 km/h. Each travelled 260 km and paid 132·9 cents per litre for fuel, using the model of car in the table.
(i)Find how much longer it took Mary to complete the journey. Give your answer correct to the nearest minute.
(d)(i)
(ii)Based on the data and their average speeds, find how much more Jane spent on fuel during the journey.
(d)(ii)
(a)In 2015 the weights of 15 year olds were normally distributed with a mean of 63·5 kg and a standard deviation of 10 kg.
(i)In 2015, Mariska (aged 15) weighed 50 kg. Find the percentage of 15 year olds who weighed more than Mariska.
(a)(i)
(ii)In 2015, 1·5% of 15 year olds were heavier than Kamal. Find Kamal's weight.
(a)(ii)
(iii)In 2016, 150 15 year olds were randomly selected; their weights were normally distributed with mean 62 kg and standard deviation 10 kg. Test the hypothesis, at the 5% level of significance, that the mean weight of 15 year olds had not changed from 2015 to 2016. State the null hypothesis and alternative hypothesis, and give your conclusion in context.
(a)(iii)
Earnings data showed that the annual income of people in full-time employment was normally distributed with a mean of €39 400 and a standard deviation of €12 920.
(a)(i)The government intends a new tax on incomes over €60 000. Find the percentage of full-time workers liable for this tax, correct to one decimal place.
(a)(i)
(ii)The government will provide a subsidy to the lowest 10% of income earners. Find the level of income at which the government will stop paying the subsidy, correct to the nearest euro (a percentile).
(a)(ii)
(iii)Later a research institute surveyed 1000 full-time workers and found a mean annual income of €38 280. Test the hypothesis, at the 5% level of significance, that the mean annual income has changed. State the null hypothesis and the alternative hypothesis, and give your conclusion in context.
(a)(iii)
(b)The institute surveyed 400 full-time farmers and found a mean income of €26 974 with a standard deviation of €5120. Assuming annual farm income is normally distributed, create a 95% confidence interval for the mean income of full-time farmers.
(b)
(c)Data on farm size are not normally distributed. The institute could take many large random samples of farm size and create a sampling distribution of the means. Give one reason why they might do this.
(c)
(d)The institute surveyed n farmers into the use of agricultural land. If the margin of error of the survey was 4·5%, find the value of n.
(d)
A survey of 100 shoppers, randomly selected from a large number of Saturday supermarket shoppers, showed that the mean shopping spend was €90·45. The standard deviation of this sample was €20·73.
(a)Find a 95% confidence interval for the mean amount spent in a supermarket on that Saturday.
(a)
(b)A supermarket has claimed that the mean amount spent by shoppers on a Saturday is €94. Based on the survey, test the supermarket's claim using a 5% level of significance. Clearly state your null hypothesis, your alternative hypothesis, and your conclusion.
(b)
(c)Find the p-value of the test you performed in part (b) above and explain what this value represents in the context of the question.
(c)
Table 1 gives details of the number of males (M) and females (F) aged 15 years and over at work, unemployed, or not in the labour force for each year in the period 2004 to 2013 (in thousands). Source: Central Statistics Office (cso.ie).
| Year | At work | Unemployed | Not in labour force | Total | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| M | F | Total | M | F | Total | M | F | Total | ||
| 2004 | 1045·9 | 738·9 | 1784·8 | 79·6 | 31·6 | 111·2 | 457·1 | 854·2 | 1311·3 | 3207·3 |
| 2005 | 1087·3 | 779·7 | 1867·0 | 81·3 | 33·5 | 114·8 | 459·5 | 846·6 | 1306·1 | 3287·9 |
| 2006 | 1139·8 | 815·1 | 1954·9 | 80·6 | 38·1 | 118·7 | 457·6 | 844·9 | 1302·5 | 3376·1 |
| 2007 | 1184·0 | 865·6 | 2049·6 | 84·3 | 39·2 | 123·5 | 472·4 | 852·7 | 1325·1 | 3498·2 |
| 2008 | 1170·9 | 889·5 | 2060·4 | 106·3 | 41·0 | 147·3 | 494·8 | 872·5 | 1367·3 | 3575·0 |
| 2009 | 1039·8 | 863·5 | 1903·3 | 234·0 | 82·4 | 316·4 | 505·6 | 874·9 | 1380·5 | 3600·2 |
| 2010 | 985·1 | 843·5 | 1828·6 | 257·6 | 98·2 | 355·8 | 529·2 | 884·6 | 1413·8 | 3598·2 |
| 2011 | 970·2 | 843·2 | 1813·4 | 260·7 | 103·4 | 364·1 | 540·1 | 881·5 | 1421·6 | 3599·1 |
| 2012 | 949·6 | 823·8 | 1773·4 | 265·2 | 108·0 | 373·2 | 546·5 | 896·9 | 1443·4 | 3590·0 |
| 2013 | 974·4 | 829·0 | 1803·4 | 227·7 | 102·3 | 330·0 | 557·8 | 895·0 | 1452·8 | 3586·2 |
(a)Suggest two categories of people, aged 15 years and over, who might not be in the labour force.
(a)
(b)Find the median and the interquartile range of the total persons at work over the period.
(b)
(c)(i)For 2006 the percentages of persons aged 15 and over at work / unemployed / not in the labour force were 57·9% / 3·5% / 38·6%. Complete the corresponding table for the year 2011, correct to one decimal place.
(c)(i)
(ii)A 2006 census showed 864 449 persons aged under 15; the 2011 figure was 979 590. Assuming none of these are in the labour force, and given that for the total population in 2006 the percentages were 46·1% / 2·8% / 51·1%, complete the table giving the percentages of the total population at work / unemployed / not in the labour force for 2011.
(c)(ii)
(iii)A commentator states that "the changes reflected in the data from 2006 to 2011 make it more difficult to balance the Government's income and expenditure." Do you agree? Give two reasons based on your calculations.
(c)(iii)
(d)Liam draws a line chart of the number of males and females at work; Niamh draws a stacked bar chart of females at work as a percentage of the total at work.
(i)Having examined both charts, a commentator states "females were affected just as much as males by the downturn in employment." Do you agree or disagree? Give a reason.
(d)(i)
(ii)Which, if any, of the two charts did you find most useful in reaching your conclusion? Give a reason.
(d)(ii)
(iii)Use the data in Table 1, for the years 2012 and 2013 only, to predict the percentage of persons aged 15 and over who will be at work in 2014.
(d)(iii)
A generic drug used to treat a particular condition has a success rate of 51%. A company is developing two new drugs, A and B, to treat the condition. They carried out clinical trials on two groups of 500 patients suffering from the condition. The results showed that Drug A was successful in the case of 296 patients. The company claims that Drug A is more successful than the generic drug.
(i)Use a hypothesis test at the 5% level of significance to decide whether there is sufficient evidence to justify the company's claim. State the null hypothesis and state your conclusion clearly.
(i)
(ii)The null hypothesis was accepted for Drug B. Estimate the greatest number of patients in that trial who could have been successfully treated with Drug B.
(ii)
Questions reproduced from State Examinations Commission Leaving Certificate examination papers,
© State Examinations Commission (examinations.ie). Gathered here for study use.
© State Examinations Commission (examinations.ie). Gathered here for study use.