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Grassland is an important breeding habitat for some birds. These birds feed on plant material and invertebrates. Biodiversity of the habitat is maintained by domestic herbivores, such as sheep, cows and goats, grazing on growing plant material.
A group of students investigated the effect of grazing by domestic herbivores on the plant biodiversity of a grassland as measured by Simpson’s Index of Diversity. They investigated two areas. One area was grazed by herbivores and the other area was not grazed for many years because it was surrounded by a fence to keep out the herbivores.
(a) State the data that the students would have collected from the grazed and ungrazed areas to calculate Simpson’s Index of Diversity.
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(b) Describe a random (unbiased) method which the students could have used to collect the data needed to calculate the biodiversity of the plant species in the two areas.
The description of your method should be detailed enough for another person to follow.
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The students also investigated the effect grazing had on the height of one particular species of plant. Their hypothesis was:
The mean height of the plant is greater in the ungrazed grassland than the grazed grassland.
(c) State the independent and the dependent variables in this investigation.
independent variable ..........................................................................................................................................
dependent variable ............................................................................................................................................ [1]
(d) Table 1.1 shows the results of their investigation.
Table 1.1
| sample number | height of plant/mm |
|---------------|---------------------------|
| | grazed area | ungrazed area |
| 1 | 586 | 858 |
| 2 | 549 | 873 |
| 3 | 526 | 864 |
| 4 | 589 | 901 |
| 5 | 545 | 847 |
| 6 | 538 | 862 |
| 7 | 573 | 864 |
| 8 | 549 | 879 |
| 9 | 604 | 864 |
| 10 | 611 | 888 |
| mean | 567 | 870 |
| mode | 549 | |
| median | 561 | |
(i) Complete Table 1.1 by writing the values of the mode and median for the ungrazed area.
......................................................................................... [1]
(ii) Use the information and formula below to calculate the standard error for these results. Give your answers to 3 significant figures.
$$\begin{align} S_M &= \frac{s}{\sqrt{n}} \\ S_M &= \text{standard error} \\ s &= \text{standard deviation} \\ n &= \text{sample size (number of observations)} \end{align}$$
grazed area: $s = 29.5$ ungrazed area: $s = 15.7$
standard error, grazed area = ..........................................................................................................
standard error, ungrazed area = ...................................................................................................... [2]
Standard error is used to calculate 95% Confidence Intervals (CI).
The values for the grazed area are 548.3 mm to 585.7 mm.
(iii) Use the formula below to calculate the confidence intervals for the ungrazed area.
$$\text{95\% CI} = \text{mean} \pm 2S_M$$
Show your working.
ungrazed area ...........................................mm to ...........................................mm [2]
(iv) State what information is gained by calculating the confidence intervals.
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(e) The students used the mark-release-recapture method to estimate the population of an invertebrate animal found living on the grassland. They used the formula: $$\frac{\text{number of animals marked in the first sample} \times \text{total number of animals in the second sample}}{\text{number of marked animals in the second sample}}$$
State two precautions the students should have taken to ensure that the results they obtained were valid.
1. ...................................................................................................................................................................
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2. ...................................................................................................................................................................
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(f) The population of an invertebrate that feeds on seeds was estimated in both the grazed and ungrazed areas. Predict which area would have the greatest population and give a reason for your choice.
choice ................................................................................................................................................................
reason ............................................................................................................................................................... [1]
Grassland is an important breeding habitat for some birds. These birds feed on plant material and invertebrates. Biodiversity of the habitat is maintained by domestic herbivores, such as sheep, cows and goats, grazing on growing plant material.
A group of students investigated the effect of grazing by domestic herbivores on the plant biodiversity of a grassland as measured by Simpson’s Index of Diversity. They investigated two areas. One area was grazed by herbivores and the other area was not grazed for many years because it was surrounded by a fence to keep out the herbivores.
(a) State the data that the students would have collected from the grazed and ungrazed areas to calculate Simpson’s Index of Diversity.
.......................................................................................................................................................................
.......................................................................................................................................................................
.......................................................................................................................................................................
.......................................................................................................................................................................
....................................................................................................................................................................... [2]
(b) Describe a random (unbiased) method which the students could have used to collect the data needed to calculate the biodiversity of the plant species in the two areas.
The description of your method should be detailed enough for another person to follow.
.......................................................................................................................................................................
.......................................................................................................................................................................
.......................................................................................................................................................................
.......................................................................................................................................................................
.......................................................................................................................................................................
.......................................................................................................................................................................
.......................................................................................................................................................................
.......................................................................................................................................................................
.......................................................................................................................................................................
....................................................................................................................................................................... [3]
The students also investigated the effect grazing had on the height of one particular species of plant. Their hypothesis was:
The mean height of the plant is greater in the ungrazed grassland than the grazed grassland.
(c) State the independent and the dependent variables in this investigation.
independent variable ..........................................................................................................................................
dependent variable ............................................................................................................................................ [1]
(d) Table 1.1 shows the results of their investigation.
Table 1.1
| sample number | height of plant/mm |
|---------------|---------------------------|
| | grazed area | ungrazed area |
| 1 | 586 | 858 |
| 2 | 549 | 873 |
| 3 | 526 | 864 |
| 4 | 589 | 901 |
| 5 | 545 | 847 |
| 6 | 538 | 862 |
| 7 | 573 | 864 |
| 8 | 549 | 879 |
| 9 | 604 | 864 |
| 10 | 611 | 888 |
| mean | 567 | 870 |
| mode | 549 | |
| median | 561 | |
(i) Complete Table 1.1 by writing the values of the mode and median for the ungrazed area.
......................................................................................... [1]
(ii) Use the information and formula below to calculate the standard error for these results. Give your answers to 3 significant figures.
$$\begin{align} S_M &= \frac{s}{\sqrt{n}} \\ S_M &= \text{standard error} \\ s &= \text{standard deviation} \\ n &= \text{sample size (number of observations)} \end{align}$$
grazed area: $s = 29.5$ ungrazed area: $s = 15.7$
standard error, grazed area = ..........................................................................................................
standard error, ungrazed area = ...................................................................................................... [2]
Standard error is used to calculate 95% Confidence Intervals (CI).
The values for the grazed area are 548.3 mm to 585.7 mm.
(iii) Use the formula below to calculate the confidence intervals for the ungrazed area.
$$\text{95\% CI} = \text{mean} \pm 2S_M$$
Show your working.
ungrazed area ...........................................mm to ...........................................mm [2]
(iv) State what information is gained by calculating the confidence intervals.
.......................................................................................................................................................................
.......................................................................................................................................................................
.......................................................................................................................................................................
....................................................................................................................................................................... [2]
(e) The students used the mark-release-recapture method to estimate the population of an invertebrate animal found living on the grassland. They used the formula: $$\frac{\text{number of animals marked in the first sample} \times \text{total number of animals in the second sample}}{\text{number of marked animals in the second sample}}$$
State two precautions the students should have taken to ensure that the results they obtained were valid.
1. ...................................................................................................................................................................
.......................................................................................................................................................................
.......................................................................................................................................................................
2. ...................................................................................................................................................................
.......................................................................................................................................................................
....................................................................................................................................................................... [2]
(f) The population of an invertebrate that feeds on seeds was estimated in both the grazed and ungrazed areas. Predict which area would have the greatest population and give a reason for your choice.
choice ................................................................................................................................................................
reason ............................................................................................................................................................... [1]
(a) State three variables which should have been standardised in this investigation.
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(b) The medical researchers made two conclusions based on the data shown in Table 2.1.
1. An increase in the number of packets smoked decreases the PEFR measurement.
2. The number of packets smoked increases with age.
State how the results from Table 2.1 support these conclusions and how they do not support these conclusions.
support
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do not support
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(c) (i) State a null hypothesis for a statistical test to find out whether the data in Table 2.1 supports the conclusion that:
An increase in the number of packets smoked decreases the PEFR measurement.
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(ii) State two ways in which the data for group 5 is less trustworthy compared with the data for the other groups.
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................................................................................................................................................................................................. [2]
(a) State three variables which should have been standardised in this investigation.
.................................................................................................................................................................................................
.................................................................................................................................................................................................
.................................................................................................................................................................................................
................................................................................................................................................................................................. [3]
(b) The medical researchers made two conclusions based on the data shown in Table 2.1.
1. An increase in the number of packets smoked decreases the PEFR measurement.
2. The number of packets smoked increases with age.
State how the results from Table 2.1 support these conclusions and how they do not support these conclusions.
support
.................................................................................................................................................................................................
.................................................................................................................................................................................................
.................................................................................................................................................................................................
.................................................................................................................................................................................................
do not support
.................................................................................................................................................................................................
.................................................................................................................................................................................................
................................................................................................................................................................................................. [3]
(c) (i) State a null hypothesis for a statistical test to find out whether the data in Table 2.1 supports the conclusion that:
An increase in the number of packets smoked decreases the PEFR measurement.
.................................................................................................................................................................................................
.................................................................................................................................................................................................
................................................................................................................................................................................................. [1]
(ii) State two ways in which the data for group 5 is less trustworthy compared with the data for the other groups.
.................................................................................................................................................................................................
.................................................................................................................................................................................................
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................................................................................................................................................................................................. [2]