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WorksheetsStatistics for Science 1 - Outcome 1 Revision Paper 2
Total questions: 18
Worksheet time: 5hrs 30mins
An experiment to determine the amount of antigen in a test solution using single radial immunodiffusion gave the following results.
Construct an appropriate diagram to investigate if there is a possible correlation between the amount of antigen and the ring diameter.
1bi. Does there appear to be a correlation between the two variables?
Yes, a strong negative linear correlation between the ring diameter (mm) and amount of antigen (µg).
Yes, a strong positive linear correlation between the ring diameter (mm) and amount of antigen (µg).
No, there is no relationship between the ring diameter (mm) and amount of antigen (µg).
Yes, a weak positive linear correlation between the ring diameter (mm) and amount of antigen (µg).
Yes, a weak negative linear correlation between the ring diameter (mm) and amount of antigen (µg).
1bii. Justify your answer to part 1bi using two correlation statistics. (select 2 that apply)
The correlation coefficient, r, is 0.982029373 which is very close to +1.
The coefficient of determination, R2, is 4.76%. This shows that 4.76% of the changes in the amount of antigen is due to the variation in Ring Diameter and 96.44% of the variation is due to other factors.
The correlation coefficient, r, is -0.982029373 which is very close to -1.
The coefficient of determination, R2, is 96.44%. This shows that 96.44% of the changes in the amount of antigen is due to the variation in Ring Diameter and 4.76% of the variation is due to other factors.
The correlation coefficient, r, is 0.053 which is very close to 0.
1c. Obtain the equation of the regression line.
y=-0.3363-2.4218
y=-2.8678x+6.5368
y=0.3363x+2.4218
y = 2.8678x - 6.5368
1d. Estimate the amount of antigen for a ring diameter of 7.5mm.
The amount of antigen produced with a ring diameter of 7.5mm is 4.94µg.
The amount of antigen produced with a ring diameter of 7.5mm is 14.97µg.
The amount of antigen produced with a ring diameter of 7.5mm is 15.10µg.
The amount of antigen produced with a ring diameter of 7.5mm is 4.89µg.
2ai. A trainee lab technician is making up saline solutions to a nominal concentration of 10%. When checked, however, it turns out the concentrations vary somewhat. Here are the results (% concentrations given) of the sample of the first 35 batches attempted.
Determine the mean of the batches.
The mean % concentration of the saline solutions is 11.71%.
The mean % concentration of the saline solutions is 11.56%.
The mean % concentration of the saline solutions is 11.49%.
The mean % concentration of the saline solutions is 11.40%.
2aii. What is the standard deviation of the % concentrations of the saline solutions?
The standard deviation of the % concentration of the saline solutions is 1.987%
The standard deviation of the % concentration of the saline solutions is 2.016%
The standard deviation of the % concentration of the saline solutions is 1.929%
The standard deviation of the % concentration of the saline solutions is 1.961%
2aiii. What is the coefficient of variation of the % concentrations of the saline solutions?
The coefficient of variation of the % concentration of the saline solutions is 0.174
The coefficient of variation of the % concentration of the saline solutions is 0.168
The coefficient of variation of the % concentration of the saline solutions is 0.170
The coefficient of variation of the % concentration of the saline solutions is 0.172
2aiv. What is the standard error of the % concentrations of the saline solutions?
The standard error of the % concentration of the saline solutions is 0.326%
The standard error of the % concentration of the saline solutions is 0.336%
The standard error of the % concentration of the saline solutions is 0.341%
The standard error of the % concentration of the saline solutions is 0.331%
2b. What is the purpose of the standard error?
The standard error is an estimate of how far the population median is from the true sample median
The standard error is an estimate of how far the sample mean is from the true population mean
The standard error is an estimate of how far the sample median is from the true population mean
The standard error is an estimate of how far the population mean is from the sample mean
2ci. What is the lower confidence interval for the dataset?
The lower confidence interval is 10.599% concentration
The lower confidence interval is 10.761% concentration
The lower confidence interval is 10.865% concentration
The lower confidence interval is 11.046% concentration
2cii. What is the upper confidence interval for the dataset?
The upper confidence interval is 12.264% concentration
The upper confidence interval is 12.382% concentration
The upper confidence interval is 12.217% concentration
The upper confidence interval is 12.201% concentration
2ciii. What do the confidence intervals mean in terms of the data?
There is a 95% confidence level that the true population mean for the % concentrations will fall between 10.865 and 12.264
There is a 95% confidence level that the true population mean for the % concentrations will fall between 11.046 and 12.382
There is a 95% confidence level that the % concentrations will fall between 10.761 and 12.217
There is a 95% confidence level that the % concentrations will fall between 10.599 and 12.201
2d i. 15.3 is which statistical measure of the dataset?
Q1
Minimum
Maximum
Q2
Q3
2d ii. 9.85 is which statistical measure of the dataset?
Q1
Minimum
Maximum
Q2
Q3
2d iii. 13.45 is which statistical measure of the dataset?
Q1
Minimum
Maximum
Q2
Q3
2d iv. 8.3 is which statistical measure of the dataset?
Q1
Minimum
Maximum
Q2
Q3
2d v. The value for the median (Q2) is....
9.45
15.5
7.95
11.7
13.8
2f. Another student’s attempts at the same task had resulted in the following 5-figure summary:
Min = 8.0% Q1 = 9.3% Q2 = 10.2% Q3 = 10.6% Max = 12.7%
Compare the efforts of the two trainees, and make two comments about the figures. (Select two that apply)
2nd trainee’s results are more consistent % concentration as there is a small spread
2nd trainee’s results are more consistent % concentration as there is a large spread
2nd trainee’s median is much lower than the first’s showing the % concentration on average are lower than the first trainee
2nd trainee’s median is much higher than the first’s showing the % concentration on average are higher than the first trainee
