Question

2. Based on the data below:

a) Plot the percentage of insects versus the natural logarithm of the dose.

b) Convert the data to probit variable, and plot the probit versus the natural logarithm of the dose.

c) Determine the probit constants and the LC50. Please show all calculations.

Dose of rotenone (mg/l)	Number of insects	Number affected (deaths)
9.1	60	47
7.0	73	51
6.4	49	32
5.3	35	20
4.4	54	18

Answer 1

Dose of rotenone (mg/l)	Log (Dose)	Number of insects	Number of deaths	% of Deaths	Probit
9.1	0.959041392	60	47	78.33333333	5.77
7	0.84509804	73	51	69.8630137	5.52
6.4	0.806179974	49	32	65.30612245	5.39
5.3	0.72427587	35	20	57.14285714	5.18
4.4	0.643452676	54	18	33.33333333	4.56

(Logarithms and percentages are calculated using Microsoft Excel)

(Percentages can be converted into probit constants using a probit table)

a)

(This plot was made using Microsoft Excel)

b)

(This plot was made using Microsoft Excel)

c) To calculate probit constants and LC50, we need to do Regression Analysis. This also can be done in Microsoft Excel. For regression, y axis is Probit and x axis is logarithm of Dose.

After doing Resgression, we get the following data:

	Coefficients
Intercept	2.381509647	b
X Variable 1	3.648133944	a

In the line   , a is the x variable and b is the y intercept.

Therefore the probit constants are:

and

Putting the values in the equation, we get:  

To find the LC50, we have to find the probit value for 50% from the table and substitute it to y.

The probit value for 50% = 5

Therefore,