Student Name:
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- Define the following terms:
- Mean: a measure of the central tendency of a set of data.
- Variability
- Standard deviation
- Errors bars show variability in data (either range of data or standard deviation)
State which two pairs of groups below can we see an overlap in the standard deviation of the data.
/ And/ And
c. In which group is the mean NOT likely to be significantly different to the mean of group 3?
-
3. On the axes below, plot the following three curves (all have a normal distribution):
a. Has the highest mean and a high standard deviation.
b. Has the lowest mean, but the highest frequency at that mean.
c. Has a mean between (a) and (b) and has the smallest standard deviation.
4. Complete the following paragraph:
± 1σ (standard deviation) from the mean represents ____ % of all the data points.
In data with a high standard deviation, data are clustered closer to/ further from the mean.
In data with a low standard deviation, data are clustered closer to/ further from the mean.
Overlapping standard deviations suggest two datasets are/are not significantly different.
___ % of all data fall within 2 standard deviations of the mean.
Group A / Group B24 / 24
25 / 29
26 / 25
23 / 23
25 / 29
25 / 32
26 / 34
27 / 31
23 / 32
23 / 29
Mean
Stdev
P= / 0.004 / (T-Test)
6. Calculate the means and standard deviations of these two groups of data (to one decimal place)
Show your working here.
7. In a t-test comparing Group A and Group B, the P value was calculated as 0.004.
What does this P value tell us about these two sets of data?
Explain your answer.
8. Why does the scientific community place so much importance on significance tests such as the t-test?
SKILLS CHECK I can calculate mean and standard deviation using:
a. A graphical display or scientific calculator
b. Microsoft Excel 2007
9. Use the t-table shown to perform the t-tests with these examples. Make sure you follow conventions and write everything down correctly each time (as in part b).
a. Which confidence limit do we normally choose in Biology? Why?
b. A student measures 15 snail shells on the north side of an island and 16 on the south.
H0 =
Confidence =
DF =
Critical value =
t is calculated as 2.02.
So we reject/accept Ho.
Conclusion:
c. A student measures the resting heart rates of 10 swimmers and 12 non-swimmers.
t is calculated as 3.65.
So:
Conclusion:
10. A researcher is investigating the link between air pollution and egg size in chaffinches. She measures the diameters of eggs at 8 sites near a factory and 9 sites out of town. The mean egg diameter by the factory was 5.6cm, whereas it was 7.4cm out of town.
t is calculated as 2.08
So:
Conclusion:
11. A doctor is testing the effectiveness of two kinds of antiseptics against bacterial cultures. He sets up six samples with antibiotic 'A' and six with antibiotic 'B' and after 2 weeks counts the numbers of bacteria present in each. Mean counts: A = 5.6x104cells; B = 5.7x104cells.
t is calculated as 1.97
So:
Conclusion:
12. A recent study looking into male fertility found that men who drank 3 cups of coffee a day showed signs of more sperm tail damage (39.1% of sperm) than those who did not (32.8%). 22 men sampled drank no coffee. 18 drank 3 or more cups a day.
t is calculated as 3.35
So:
Conclusion:
9. Look at the graph below:
13. Identify the true statements, according to the graph:
a. There is no correlation between number of cellphones and number of students with asthma.
b. There is a positive correlation between number of cellphones and asthma cases.
c. There is a negative correlation between number of cellphones and asthma cases
d. Increased numbers of cellphones cause an increase in numbers of students with asthma.
e. Increased numbers of asthmatic cause increased numbers of cellphones in a school.
f. There is no evidence of causality in this graph.
14. Suggest two comparisons in which a causal relationship is likely
(e.g. temperature and rate of reaction).
14. Calculate the mean and standard deviation for each set of data. Make a line graph with error bars. Do the T-test comparing pH of 6 and 8.
pH 5 / pH 6 / pH 7 / pH 8 / pH 99 / 10 / 10 / 10 / 9
8 / 9 / 10 / 9 / 9
7 / 8 / 10 / 9 / 8
7 / 8 / 10 / 10 / 8
9 / 9 / 10 / 9 / 8
IV: pH
DV: number of germinating seeds (out of 10)
15. Calculate the mean and standard deviation for each set of data. Make a line graph with error bars. Do the T-test comparing 12 and 18 hours of light.
0 hrs / 6 hrs / 12 hrs / 18 hrs / 24 hrs2.1 / 8.3 / 10.5 / 11.7 / 10.1
0 / 10.2 / 18.3 / 11.5 / 12.4
4.7 / 9.6 / 7.1 / 12.0 / 9.7
1.1 / 10.5 / 12.3 / 11.2 / 8.1
3.2 / 8.8 / 11.8 / 11.6 / 14.3
IV: hours of light
DV: growth (cm) at 72 hours
Stephen Taylor Bandung International School