Statistics Questions Practice W2 Final 1

Practice for Statistics / VIHS / Department of Biology 1

Year Test Year

Jan 2003 Q1 t test Jan 2008 Q11 Correlation

June 2003 Q2 Correlation June 2008 Q12 t test

Jan 2004 Q3 t test Jan 2009 Q13 t test

June 2004 Q4 Correlation June 2009 Q14 U test

Jan 2005 Q5 …………. Specimen Q15 …………

June 2005 Q6 U test June 2010 Q16 t test

Jan 2006 Q7 Correlation Jan 2011 Q17 Correlation

June 2006 Q8 ………….. Jan 2012 Q18 Correlation

Jan 2007 Q9 W test June 2012 ?????????????? June 2007 Q10 t test

Jan 2003 Q1. Auxins are plant growth substances which can cause elongation in developing plant tissues. A student formed the hypothesis that an increase in the concentration of auxins would increase the elongation of seedling tissue. To test this idea he cut twenty 15 mm lengths from identical oat seedlings and immersed ten of them in a

solution of 1 µg dm–3 auxin and ten in a solution of 10 µg dm–3 auxin.

These samples were left in controlled conditions for 12 hours, after which they were removed and their lengths re-measured. An extract from his laboratory notebook is shown below.

1 g dmall 15 mm

remeasured lengths22 25 24 23 22

20 25 24 23 24

10 g dmall 15 mm

Remeasured lengths25 28 26 27 25

26 29 24 26 23

–3

–3


(a) Prepare a table and organise the data in a suitable way so that the increase in length in each concentration can be compared. (4) (b) Use the data in your table to present the information in a suitable graphical form. (c) State a suitable null hypothesis for this investigation. (1) (d) The student applied a t-test to his data to test his hypothesis. He calculated the value of t to be 3.68. The table below shows the critical value of t with 18 degrees of freedom for various significance levels.

Significance level (%) 20 10 5 2 1

Critical value of t 1.33 1.73 2.10 2.55 2.80

What conclusions can be drawn from this investigation? Use the information provided to explain your answer. (3) (Total 11 marks) …………………………………………………………………………………………………. June 2003 Q2. Mayfly nymphs are immature insects that live in freshwater streams. In a pilot study of their distribution, a student noticed that she could distinguish two types, because they possessed structural differences. One type, which she described as flattened mayfly nymphs, appeared to be more abundant in fast-moving water than in still water. Using this observation, she formed the hypothesis that the number of flattened mayfly nymphs would increase as the speed of the current increased. In order to test this idea, she counted the flattened mayfly nymphs at 13 sites on the

same stretch of river. Each site had an area of 1 m2. She repeated this at the same sites one week later. At each site, the speed of the water was measured in metres per second. It was measured on the first occasion only, since the stream was running at the same level when sampling was undertaken on the second occasion. The record of her fieldwork data is shown below.

Site

number

First sample

Number of

flattened

nymphs

Second sample

Number of

flattened

nymphs

Speed of

water

metres per

second

1

2

3

4

5

6

7

8

9

10

11

12

13

14

9

11

1

0

6

8

6

3

1

0

0

1

0.80

0.55

0.40

0.22

0.25

0.24

0.35

0.21

0.20

0.15

0.10

0.11

0.13

12

11

7

1

0

10

14

8

1

1

0

0

1


(a) Prepare a table and organise the data in a suitable way to show the relationship between flow rate and the number of flattened mayfly nymphs. (4) (b) Use the data in your table to present the information in a suitable graphical form. (c) State a suitable null hypothesis for this investigation. (1) (d) The student applied a correlation test to the data to find out whether they supported her hypothesis. The correlation coefficient was found to be 0.797. The table below shows critical values for correlation coefficients at the p = 0.05 and 0.01 levels.

Number of pairs of measurements

Critical value at p = 0.05

Critical value at p = 0.01

8 0.738 0.881

9 0.683 0.833

10 0.648 0.794

11 0.620 0.785

12 0.591 0.777

13 0.567 0.746

14 0.544 0.715

15 0.525 0.691

What conclusions can be drawn from this investigation? Use the information provided to explain your answer. (3) (Total 11 marks)

………………………………………………………………………………………………….


Jan 2004

Q3. A student noticed that on two fields, one with horses grazing and the other with cattle, differences were apparent between the number of elder seedlings growing in each field. She thought that there were more elder seedlings growing in the field grazed by horses than in the field grazed by cattle. To test this hypothesis, she counted the numbers of elder seedlings at 20 random sites in each field using a

0.25 m2 quadrat. A record of her field studies is shown below

Numbers of elder seedlings in

areas of 0.25 m2 where horses graze

18 12 16 22 8 9 21 4 17 5

9 15 17 23 13 14 10 14 14 16

Numbers of elder seedlings in

areas of 0.25 m2 where cattle graze

10 8 8 3 4 6 9 18 1 14

8 5 10 2 12 13 7 17 9 11

(a) Organise these data into two tally charts, one for each field. Group the data into suitable size classes to enable you to compare the numbers of seedlings in each field. (4) (b) Use the data in your table to present the information in suitable graphical form. (c) State a suitable null hypothesis for this investigation. (1) (d) In order to determine if her data supported her hypothesis, the student applied a t-test. This statistical test determines whether the difference between two means is significant. A t-value of 3.71 was calculated. The table below shows critical values for t with 38 degrees of freedom for various significance levels.

Significance level % 20 10 5 2 1

Critical value of t 1.30 1.68 2.02 2.42 2.70

What conclusions can be drawn from this investigation? Use the information provided to explain your answer. (3) (Total 11 marks)

………………………………………………………………………………………………….


June 2004 Q4. Whilst investigating the distribution of plants on coastal sand dunes, a student noticed that reeds only seemed to grow in the low-lying areas where the soil was wet. He formed the hypothesis that the number of reeds growing in the area increased as the water content of the soil increased. To test his hypothesis, he

selected an area of wet soil where there were many reeds growing. Using a 0.25 m2 quadrat, he laid out a belt transect from this area into the surrounding drier soil. He placed 8 quadrats along the transect and counted the number of separate reed plants in each quadrat. He also took a small sample of soil from exactly the same depth from the centre of each quadrat. To find the water content, he weighed each soil sample, then dried it in an oven and reweighed it. An extract from his field records is shown below.

Reed plants in each quadrat

1 2 3 4 5 6 7 8

14 13 10 11 7 8 5 0

Soil sample results Wet mass

1 81.7g

2 80.2g

3 80.5g

4 81.9g

5 79.9g

6 80.1g

7 80.4g

8 80.3g

Mass after drying in the oven

1 58.2g

2 57.0g

3 57.8g

4 60.1g

5 61.2g

6 68.7g

7 72.1g

8 74.5g

(a) Calculate the percentage water content of each of the soil samples. Then prepare a table and organise the data in a suitable way so that the percentage water content of the soil can be related to the number of reed plants. (4) (b) Use the data in your table to present the information in a suitable graphical form. (c) To test the relationship between soil water content and the number of reed plants, the student used a rank correlation coefficient. Calculate the rank correlation coefficient (rs) for these data using the information

given below. Show your working.

rs = 1 – 1–nn

D6

2

2

Where

ΣD2 = 6 and n = the number of samples (2)


(d) The critical value of rs at p = 0.05 for this investigation is 0.738. Using your

calculated value of rs, what conclusion concerning the relationship between soil

water and number of reed plants can be drawn from this investigation? (1) (Total 11 marks) ………………………………………………………………………………………………… Q5. Jan 2005 – no paper available …………………………………………………………………………………………………. June 2005 Q6. Lichens are plant-like organisms that may grow on the surface of tree trunks. After a pilot study of their distribution on trees, a student produced the hypothesis that one type of lichen grew larger on birch trees than on oak trees. For the main study, the student selected eleven trees of each species. She placed a 50 cm × 50 cm quadrat one metre from the ground on the south facing side of one of them. She then selected the largest lichen of her chosen type inside the quadrat, and measured its width at its widest point. This technique was repeated for each of the selected trees. An extract from the student’s field record is shown below.

Width of lichens on birch

55mm 24mm 21mm 18 mm 60mm 8 mm

35mm 22mm 33mm 16 mm 28mm

Width of lichens on oak

15mm 20mm 6 mm 14 mm 16mm

33mm 9 mm 13mm 19 mm 45mm 12mm

(a) Prepare a table of the raw data and organise it in such a way that the median width of these lichens on each species of tree can be identified. (4) (b) Use the data in your table to present the information in a suitable graphical form. (c) State a null hypothesis for this investigation. (1) (d) The student decided to apply the Mann-Whitney U test to the data. This statistical test determines if the difference between the medians is significant. The calculations produced two U values, U1 = 92 and U2 = 29. In order to support her

hypothesis, the smaller U value is required to be the same as, or less than, the critical value. The table below shows the critical values for the Mann-Whitney U test at the p = 0.05 level.


Sample size n2

8 9 10 11 12 13

Sample size n1

8

9

10

11

12

13

13

15

17

19

22

24

15

17

20

23

26

28

17

20

23

26

29

33

19

23

26

30

33

37

22

26

29

33

37

41

24

28

33

37

41

45

Use the information above to draw conclusions from this investigation. (3) (Total 11 marks)

…………………………………………………………………………………………………. Jan 2006 Q7. Hawthorn is a common shrub found in hedgerows. Its leaves have many indentations as shown in the photograph below.

A student formed the hypothesis that the larger leaves would have deeper indentations. To test this hypothesis she collected twelve leaves from a single branch of the shrub. Then she obtained the surface area of one side of each leaf by drawing its outline on graph paper and counting the number of squares it covered. Finally she measured the depth of each indentation as shown below.


The results of her investigation are shown below.

Leaf 1 Area 271 mm2 Leaf 2 Area 306 mm2

Indentation depths 16, 5, 7, 14 mm Indentation depths 20, 6, 7, 17, 4 mm

Leaf 3 Area 245 Leaf 4 Area 184

Indentation depths 4, 13, 5, 5, 13, 4 Indentation depths 9, 10


Indentation depths 15, 5, 5, 15 Indentation depths 10, 5, 6, 10


Indentation depths 3, 10, 3, 3, 11, 3 Indentation depths 3, 10, 12, 3


Indentation depths 10, 6, 2, 5, 13 Indentation depths 2, 10, 10, 12


Indentation depths 9, 8, 3 Indentation depths 10, 4, 2, 7

(a) Calculate the total indentation depth for each leaf. Then prepare a table and present the results in a suitable way so that the surface area of each leaf can be compared with its total indentation. (4) (b) Use the data in your table to present the information in a suitable graphical form. (c) To test the relationship between the leaf surface area and the total indentation depth, the student used a rank correlation coefficient. Calculate the rank correlation coefficient (rs) for these data using the information given below. Show your working.

nn

D61r

3

2

s

Where ΣD2 = 44 n = the number of samples (2)


(d) The critical value of rs at p = 0.05 for this investigation is 0.54. Using your

calculated value of rs, what conclusion concerning the relationship between leaf

surface area and total indentation depth can be drawn from this investigation? (1) (Total 11 marks)

…………………………………………………………………………………………………. Q8. June 2006 – no question available …………………………………………………………………………………………………. JANUARY 2007 Q9. Skylarks are birds in the British Isles that are in serious decline. A sixth form student assisted in a piece of research to determine if the height or wheat stems left after harvesting affected the number of skylarks. The study was conducted between October and March. Ten separate fields, numbered 1-10, were used on different farms. An area of two hectares in each field was fenced. This area was divided into two plots, each of one hectare. In late October, one plot in each field was randomly selected and the wheat stems were cut to reduce their height. The other plot contained uncut stems and acted as a control. Five visits were made to each field in a randomly selected sequence. Each time, the numbers of skylarks were estimated by walking parallel transects across cut and uncut plots and counting the number of birds that flew out from each of them. An extract from the student’s field record is shown below.


(a) For each field. Calculate the mean number of skylarks in the plot with cut wheat stems and the mean number of skylarks in the plot with uncut wheat stems. Prepare a table that includes the raw data, so that the means for each field can be compared. (4) (b) Use the data in your table to present the data in a suitable graphical form. (3) (c) State the null hypothesis for this investigation. (1) (d) The student decided to apply the wilcoxon signed rank test to the paired data. This statistical test uses the differences between paired samples and is equivalent to a t-test for paired data. The calculations produced a w value of 7. In order to support the student's hypothesis, the w value is required to be less than the critical value. The table below shows the critical values for the wilcoxon signed rank test at the p = 0.05 level.

Use the information in the table to draw conclusions from this investigation. (3)

(Total 11 marks) ……………………………………………………………………………………………………... JUNE 2007 Q10. Marram grass (Ammophila arenaria) is a grass-like plant which grows in the soft sand of dunes close to the sea. It grows through the sand by means of horizontal underground stems. These stems have swellings at intervals which are called nodes. The distance between two nodes is called an internode as shown in the drawing below.


Sand dunes are affected by strong winds which move the sand and bury the stems of Marram grass. Where the effect of wind is stronger the stems are buried deeper and they grow faster, making the internodes longer. A student formed the hypothesis that the first internodes on the stems of Marram grass would be longer on the windward (exposed) side of dunes, compared to those on the sheltered side. To test this hypothesis she measured the length of the first internodes on underground stems from carefully controlled samples on each side of two dunes. An extract from her field note book is shown below. First internode length in mm Dune 1 Sheltered 70, 36, 90, 10, 50, 90, 40, 52 Windward 80, 107, 82, 97, 70, 74, 115, 60 Dune 2 Sheltered 41, 84, 29, 31, 37, 56, 41, 62 Windward 108, 110, 79, 71, 50, 92, 82, 61 (a) Prepare a table of raw data and organise it in such a way that the distribution of size classes of first internode lengths on the windward side of the dune can be compared with those on the sheltered side. (b) Use the data in your table to present the information in a suitable graphical form. (c) Comment on the variability shown by these data. (1) (d) The student applied a t-test to her data in order to test this hypothesis. She calculated the value of t to be 4.09. The table below shows the critical values of t with 30 degrees of freedom at different

What conclusions can be drawn from this investigation? Use the information provided to explain your answer. (3)(Total 11 marks) …………………………………………………………………………………………………… JANUARY 2008 Q11. Dogwhelks (Nucella Iapil!us.a are carnivorous snails that live on rocky shores. Barnacles. Which are small filter-feeding crustaceans, are their main prey. The barnacles fix themselves permanently to rocks on these shores. A student formed the hypothesis that the distribution of dogwhelks was determined by thce availability of their main food source. To test this hypothesis. She placed a 1 m2 quadrat at eight random points at one level along a rocky shore. The number of dogwhelks inside each quadrat was counted. However, the student decided that.


Barnacles were small and too numerous to count accurately in such a large area. Therefore, she counted their numbers in five separate 5 cm x 5 cm quadrats placed randomly inside the 1 m2 quadrat at each of the eight sites. The results of her investigation are shown below.

(a) Use the barnacle counts to estimate the total number of barnacles in each 1 m2 quadrat. Prepare a table and present the results in a suitable way so the number of dogwhelks And the number of barnacles in each 1 m2 quadrat can be compared. (c) Use the data in your table to present the information in suitable graphical form. (c) To test the relationship between numbers of dogwhelks and barnacles, the student used a rank correlation coefficient. Calculate the rank correlation coefficient (rs) for these data using the information given below. Show your working.

n = the number of samples (2) (d) The critical value of rs, at p = 0.05, for this investigation is 0.738. Using your calculated value of rs, what conclusion concerning the relationship between the number of dogwhelks and number of barnacles can be drawn from this Investigation?

(Total 11 marks) ……………………………………………………………………………………………………...


JUNE 2008 Q12. Wood sorrel is a common plant of woodland. Its leaves respond to decreasing light intensity by showing ‘sleep’ movements, in which leaflets fold towards the leaf stalk. Increasing light intensity causes these movements to be reversed. A student investigated these movements by using plants from two different woodland habitats, one that was more shaded than the other. He took ten samples from each of these habitats and placed their leaf stalk in tubes containing water. These were left in the dark until the leaflets were fully folded towards the stalk. He then exposed the samples to the same light intensity for twenty minutes. After this time he measured the angle between the stalk and one of the leaflets for each of the twenty samples using a special protractor as shown in the diagram below. The opening angle was recorded in degrees and minutes. One degree is divided into 60 minutes.

A copy of the student’s notebook, with the opening angles of wood sorrel from the two habitats, is shown below.


(a) Calculate the opening angles in decimal format (e.g. 70° 45 mins = 70.75°) and prepare a table to show these angles, together with the mean opening angle of leaflets, for each of the two habitats. (b) Use the information in your table to present the data in a suitable graphical form. (c) State a suitable null hypothesis for this investigation. (1) (d) A t-test was applied to these data to determine whether the means of each group were significantly different. A t-value of 3.62 was calculated. The table below shows critical values for t with 18 degrees of freedom for various levels of significance.

What conclusion can be drawn from this investigation? Use the information provided in the table to explain your answer. (2) (e) Describe three limitations of this method that could affect the reliability of the results. (3) (Total 11 marks) ……………………………………………………………………………………………………...


JANUARY 2009 Q13. Daisies are flowering plants frequently found growing amongst grasses on lawns. A student earned money by cutting the grass on the lawns of his neighbours. Each neighbour supplied a lawn mower. These were of two types: those that had a box to collect Grass cuttings and those that did not. He noticed that there appeared to be more daisies plants on lawns where the grass cuttings were left on the surface. He set up a controlled investigation to test whether this observation was significant. He Took a random selection of four lawns which were cut using a grass box and four which were cut without a grass box. On each lawn he used a randomly placed 0.5 × 0.5 metre quadrat divided into 25 smaller squares. He counted the number of smaller squares in which daisies were present. This Was then repeated ten times for each lawn. The raw data from his investigation are shown below.

(a) Prepare a table that summarises both the number of daisies in the squares in each law and the mean number in each type of lawn. (3)


(b) Use the data in your table to present the information in suitable graphical form so that the distribution of daisies can be compared. (c) A t-test was applied to determine whether the mean numbers of daisies on lawns cut with the two types of mower were significantly different. A t value of 3.81 was calculated. The table below shows the critical value for t with 78 degrees of freedom for various levels of significance.

What conclusion can be drawn from this investigation? Use the information in the table to explain your answer. (2) (d) Use the information in your table and graph to comment on the variability of the data collected and how this may affect the reliability of this investigation. (3)(Total 11 marks) ……………………………………………………………………………………………………..


JUNE 2009 q14. Catclaw mimosa (Mimosa pigra) is a plant which may form dense thorny thickets as high as 6 metres. It is an invasive weed in Northern Australia, where it is a hazard to livestock. One method used to control it is by the use of stem-mining moths. Plants infected by moths produce fewer seeds, but this may not be effective in all habitats. A group of students tested the effectiveness of this method of biological control in two habitats: a floodplain and a woodland. Both habitats had catclaw mimosa plants growing in them. The students selected two sites in each habitat. In each habitat, one site had mimosa plants that were infected with stem-mining moths and the other had no infection. At all four sites, eleven permanent 0.5 × 0.5 m quadrats had been prepared and the students collected the top 2 cm of soil from each. They sieved the soil and counted the total number of mimosa seeds they found in each sample. The raw data table compiled by the students is shown below.

(a) Prepare a table of the raw data and organise it in such a way that the median number of seeds with and without stem-mining moths in each of the habitats can be identified. (b) Use the data in your table to present the information in a suitable graphical form so that the effects of the moths in the two habitats can be compared. (c) State a suitable null hypothesis for this investigation. (1) (d) The students decided to apply the Mann-Whitney U test to the data. This statistical test determines if the differences between the medians is significant. The calculations produced two U values for each set of data. In order to support a difference between the numbers of seeds produced by infected and non-infected plants


in each habitat, the smaller U value is required to be the same as, or less than, the critical value. For the floodplain sites these values were U1= 119 and U2= 2 and for the woodland sites these values were U1= 36 and U2= 85. The table below shows the critical values for the Mann-Whitney U test at the p = 0.05 level.

What conclusion can be drawn from this investigation? Use the information in the table to explain your answer. (2) (e) What other conclusion, concerning the effectiveness of this type of biological control in different habitats, can be made from these data? (1)(Total 11 marks) ……………………………………………………………………………………………………... Specimen paper Q15. The diagram below shows some limpets. Limpets are cone-shaped molluscs which are found attached to rocks on many seashores.

Some students carried out an investigation to compare the shape of limpets on a sheltered shore with their shape on a shore exposed to the action of waves. They measured the height (H) and length (L) of 15 limpets on each shore. They then used the ratio of height to length to describe the overall shape of the limpets.


An extract from their field records is shown below.

(a) Prepare a table and organise the data in a suitable way so that the range of shapes of limpets on the two shores can be compared. (4)

(b) Use the data in your table to present the information in a suitable graphical form. (c) Name the statistical test you would use to analyse your data. (1)

(d) What conclusions can you draw from this investigation? (2) (Total 11 marks)

………………………………………………………………………………………………… JUNE 2010 Q16. Red blood cells (erythrocytes) transport oxygen from the alveolar surface in the lungs to the respiring tissues. A group of nine athletes (A to I) wanted to see if training for two weeks at a mountain camp, 2000 m above sea level, had an effect on the number of red blood cells in their blood. Samples of blood were taken from each of the athletes at their normal training camp at sea level. Blood samples were taken again after two weeks of training at the mountain camp. A copy of the raw data collected is given below:


Number of red blood cells x1012 per dm3 blood before mountain training A 5.0 B 5.1 C 4.9 D 5.3 E 5.4 F 5.0 G 4.8 H 5.1 I 5.5 Number of red blood cells x1012 per dm3 blood after mountain training A 4.9 B 5.3 C 5.7 D 5.5 E 5.6 F 5.4 G 5.3 H 5.6 I 5.1 (a) Write a null hypothesis for this investigation. (1) (b) Calculate the difference in the number of red blood cells before and after the mountain training for each athlete. Prepare a table to display the raw data and your calculated values. (4) (c) Identify an anomalous result in the data from the athletes. (2) Give one reason for your answer. (d) Calculate the mean number of red blood cells per dm3 of blood for the group of athletes before and after mountain training. (2) Mean number of red blood cells before training ......................................................... Mean number of red blood cells after two weeks training at 2000 m........................ (e) Present the calculated mean red blood cell counts in a suitable graphical form. (f) A t-test was applied to the data to test the null hypothesis. The calculated value of t was 2.24. The table below shows the critical values of t with 16 degrees of freedom, at different significance levels.

What conclusion can be drawn from this investigation? Use the information in the table to explain your answer. (3)

(Total for Question 2 = 15 marks) ………………………………………………………………………………………………….


JAN 2011 Q17. Rennin is an enzyme, found in the stomach of mammals, that can form solid clots in milk. Rennin is often used in the first stage of cheese production. A student was interested in discovering which conditions would be ideal for making cheese. She wanted to determine which concentration of rennin was likely to give her suitable rates of clotting of milk. She prepared the following test tubes:

Fourteen test tubes with 5 cm3 milk

Twelve test tubes, each containing 5 cm3 of different concentrations of rennin

Two test tubes with 5 cm3 distilled water She placed these test tubes in a water bath at 30°C and left them for 10 minutes. The content of each test tube containing milk was added to a test tube containing either rennin or distilled water. These were mixed and returned to the water bath. The time taken for the milk to clot (thicken) was recorded. A copy of the student’s raw results are below.

(a) Explain why the test tubes containing milk, rennin and distilled water were left in the water bath for 10 minutes before they were mixed. (1) (b) Convert the times recorded into the SI units of seconds and prepare a suitable table to display these raw results and each of the following. (i) The mean time for clotting for each concentration of rennin. (ii) The mean rate of milk clotting, calculated using the equation below

(5) (c) Show the effect of changing the rennin concentration on the mean rate of milk clotting, in a suitable graphical form. (3) (d) Identify an anomalous result in the data for the different rennin concentrations. Give one reason for your answer. (e) The student applied a Spearman rank correlation to explore the relationship between the rate of clotting and the rennin concentration. From her calculation, she obtained a Spearman rank correlation of 1.0. Table of significance levels for Spearman rank correlation.

What conclusion can be drawn from this investigation? Use the information in the table to explain your answer. (2)


(f ) Give an explanation for the relationship between rennin concentration and the rate of clotting of milk. (2)

(Total for Question 2 = 15 marks) ………………………………………………………………………………………………… JAN 2012 Q18. A student investigated the effect of caffeine concentration on the heart rate of animals. He selected five Daphnia (A to E), and measured the heart rate, in beats per minute, of each of them in water. This was repeated using six concentrations of caffeine solution (0.01%, 0.1%, 0.5%, 1.0%, 2.0%, 5.0%). A copy of his raw results (starting from water (0%) on the left increasing to 5% caffeine solution on the right) for each Daphnia is shown below.

(a) Write a suitable null hypothesis for this investigation. (1) (b) State and explain one ethical reason why the student chose to use Daphnia for this investigation. (2) (c) Calculate the mean heart rates for each concentration of caffeine. (3) Mean heart rate at 0.0% caffeine concentration ......................................................... Mean heart rate at 0.01% caffeine concentration ........................................................ Mean heart rate at 0.1% caffeine concentration ........................................................ Mean heart rate at 0.5% caffeine concentration ....................................................... Mean heart rate at 1.0% caffeine concentration ....................................................... Mean heart rate at 2.0% caffeine concentration ........................................................ Mean heart rate at 5.0% caffeine concentration ........................................................ (d) Prepare a table to display the raw data and your calculated values for the mean heart rates. (3) (e) On the graph paper below, draw a suitable graph to illustrate the effect of caffeine concentration on the mean heart rate of Daphnia. (3) (f ) The student used a statistical test to investigate the significance of the correlation between the mean heart rates and the caffeine concentrations. His calculation gave a correlation value of 1.00. The table below shows significance levels and correlation values for this statistical test.


What conclusions can be drawn from this investigation? Use the information provided in the table above and in the graph you have drawn, together with your knowledge and understanding, to explain your answer. (4)

(Total for Question 2 = 16 marks)

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Statistics Questions Practice W2 Final 1