How Science Works (HSW) & Math skills

Question 1

Valid conclusions need……

Answer 1

Need:

• Large sample size SO representative
• Long study SO can allow…. / see effect of X
• Control used SO comparison can be made.
  *Mean & SD SO significant differences can be determined.

Question 2

When the patients recorded the intensity of pain, suggest two reasons why it was important to use a statistically valid scale.

Answer 2

• Pain perception is subjective / pain threshold varies
• To ensure that differences (in pain detection) were (statistically) significant / differences not due to chance
• For (valid) comparison;

Question 3

Limitations:

You can only use the information provided.

Answer 3

• Small sample size, not representative;
• Only sampled males, females may respond differently to treatment;
• Only tested on …….. in a lab, in the wild, may obtain different pattern in data;
• Only tested on …….. species, might not be true for all species;
• No STATS test so differences could be due to chance;
• Data is SUBJECTIVE, some people may have lied

Question 4

Null hypothesis (How to write one)

Answer 4

• [x] will have no effect on [y]
• E.g. Temperature will have no effect on rate of reaction
• There will be no correlation between age and weight
• There will be no difference between the observed and expected ratio of 3:1 brown eyes to blue eyes

Question 5

Explain why a log scale is used to record the number of cells/bacteria.

Answer 5

• Large range/difference/increase in numbers;
• Accept reference to exponential (increase)

Question 6

In the UK in 2017, there were 805 000 deaths.

Cancer caused 29% of all deaths.

Throat cancer caused 4% of all deaths from cancer.

Calculate the mean number of people who died of throat cancer per month in 2017.

Answer 6

778

(805 000 x 0.29 x 0.04) / 12

Question 7

Information travels at 120 metres per second in neurones.

Calculate the time it would take for the information to travel 1.8 m along a neurone.

Give your answer in milliseconds (2 sig fig)

Answer 7

15 ms

(1.8/120) x 1000

Question 8

A ruler has an error of ± 1 mm.

An object’s length was 5.7 mm.

Calculate the % error of uncertainty.

to 2 DP

Answer 8

17.54 %

Question 9

What is the equation for uncertainty of a measurement?

Answer 9

Reading: (half of smallest interval / reading) * 100

Meauremement: (one interval / actual measurement) *100

Question 10

Calculate the percentage change in mass [grams]:

Mass before = 6.3 g

Mass after = 2.4 g

Answer 10

(Difference / Original) x 100

(3.9 / 6.3) *100

= 61.9 %

Question 11

Calculate the mean value:

8.4, 2.5, 4, 1.1, 8.5, 8.5, 7, 2.5, 7.9

Answer 11

8.4+2.5+4+1.1+8.5+8.5+7+2.5+7.9
________________________________________
9

= 5.6

Question 12

Which P value(s) shows a difference is significant.

a) P=0.06
b) P>0.05
c) P<0.05
d) P<0.50

Answer 12

c) P<0.05

The probability that the difference is due to a random chance event is less than 5%

Question 13

A scientist determined the volume of a plant cell and the volume of organelles it contained.

They found:

• the volume of a plant cell is 18 500 µm3
• the volume of all the mitochondria in a plant cell is 262.5 µm3
• the volume of all the mitochondria and all the chloroplasts in a plant cell is 46.1% of the volume of a plant cell.

Use this information to calculate the volume of all the chloroplasts in a plant cell.

Answer 13

8266 µm3

18 500 x 0.461 = 8528.5;

8528.5 - 262.5;

Question 14

Define Standard Deviation.

Answer 14

The spread of data around the mean

Question 15

Large SD bars indicate…….

Answer 15

A large range of variation in the data.
Less reliable mean value.

Question 16

Explain the advantage of showing the data using standard deviations rather than ranges.

Answer 16

1. SD is spread of data around the mean;

Accept: range is difference between highest and lowest values/extremes or range includes anomalies/outliers.

2. (SD) reduces effect of anomalies/ outliers;

Reject: (SD) removes anomalies/outliers.

3. (SD) can be used to determine if (difference in results is) significant/not significant/due to chance /not due to chance; or allows a STATS test to be performed to determine if differences are significant.

Question 17

Which stats test would you use if the data is categoric?

Answer 17

CHI SQUARED

Question 18

Which stats test would you use to see if there is a relationship between two variables?

Answer 18

Correlation coefficient
Spearman’s Rank

Question 19

Which stats test would you use to see if there is a difference between two means?

Answer 19

Student T test

Question 20

If Y = 16.56 find the value of x

y = 0.72x + 4

Answer 20

x= 17.4

Question 21

The scientists measured the percentage change in tumour volume.

Suggest why they recorded both percentage change and tumour volume.

Answer 21

Percentage change: To allow comparison as tumours may differ in volume/size
Tumour volume: (As) tumours may differ in length/width/shape OR
(As) volume is (best) indication of the number of cells in tumour;

Question 22

Drug X is delivered at a dosage of 3 ng Kg-1h-1 for 8 days into a patient.

1ng = 1 x10-9 g

Calculate the total mass in grams of drug X injected after 8 days into a patient with a body mass of 82 kg.

[2]

Answer 22

5x10-5;;

3 x (8x24) x 82 = 47232;

47232 / 1 000 000 000;

Question 23

The concentration of ATP in skeletal muscle is approximately
5 × 10–3 mmol g–1

During maximum exercise, ATP in skeletal muscle is used at a rate of approximately 3.7 mmol kg–1 s–1.

Calculate how long maximum exercise would last if ATP was not resynthesised.

Answer 23

1.35 or 1.4 seconds;;

5x10-3 mmol g-1 x 1000 (Unit conversion)

5/3.7 = 1.35 seconds

Concentration available:

Question 24

Explain how the researcher could use her raw data to find the mode and range?

Answer 24

Mode: (Find) the most common result;

Range: Highest and lowest result;

Question 25

When would you use the MEDIAN value?

Answer 25

Small sample with anomolous data at one extreme