Statistics for Science 1 - Outcome 1 Revision Paper 2

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