Question# 1) You are conducting a dose-response experiment on a new rodenticide with 200 mice per treatment group. In one treatment group, 184 mice survived the treatment. What is the probit value for with treatment? The error interval is +/- 0.05 probit units.

Question #2: Suppose a pharmaceutical has an ED₅₀ of 57.9 mg/kg and a TD₅₀ of 433.2 mg/kg, then what is the therapeutic index for this chemical?

Question#3: Nicotine is a surprisingly toxic chemical despite its common use in society. Nicotine over-doses are becoming more common with the advent of vapor products that sell concentrated nicotine. Assume the LD₅₀ for nicotine is 1.13 mg/kg. Then how much nicotine (in mg) would be needed to give a 77.0 kg person a 50:50 chance of dying?

Question#4: Suppose you conducted a dose response experiment and plotted as a graph with the standard axes (log(dose) on X-axis and Probit on y-axis). The resulting regression line was y = 1.28x + 0.96. Calculate the TD₅ for this chemical (where 5% of the population responds). The units are the standard chronic units of dose, namely mg/kg*day. The error interval is +/- 2 mg/kg*day.

Question#5: Suppose someone really hated rats and wanted to make sure they died with 98 % probability after a single feeding. Assuming the rat weighs 0.59 kg, then how much arsenic (in mg) is needed given that the dose-response regression line for arsenic is: y = 1.8453x + 4.3394 (in the standard format of: probit = (slope)(log dose) + intercept)? The units of the dose in the dose-response curve are mg/kg.

Question#6: Suppose you are conducting a dose-response study for a detergent that might be released to the environment. You select the fathead minnow as your test subject. You raise 20 minnows in each of 6 test populations. One group is treated as a control (no chemical added) while the other 5 populations were treated with 5, 10, 50, 100, and 300 mg/L. After 96 hours, the test populations were scored for mortality. The results were:

Dose (mg/L)	Number dead (out of 20)
0	0
5	2
10	3
50	7
100	11
300	15

Calculate the LD₃₀ for this chemical.

You may need to extrapolate beyond your dose-response curve for this question.

Question #7: You are conducting a dose-response study for a new chemical and you are using 100 mice per treatment group. You conduct the experiment and get the following data:

Dose (mg/kg)	Number dead
0	1
1	1
3	1
6	3
10	14
20	38
40	73
80	94
100	98

Calculate the LD₉₀ for this compound.

Question#8: You are working on developing a new sleep aid drug that does not have many of the side effects of the current drugs. You received permission to conduct a human trial where you were able the give doses of the chemical to the same group of test subjects (n= 50) once a week (so that the chemical is fully cleared from their systems before getting another dose). Anyone who fell asleep within 20 minutes was called a response. The results were as follows:

Dose (mg)	Number responding (out of 50)
0	5
5	6
10	4
25	10
50	18
100	24
200	33
500	39

Calculate the ED₆₀ for this new medication. You may need to extrapolate beyond your dose-response curve.

Question#9: A company is working to develop a new herbicide that may be safer for the environment, but its effectiveness needs to be determined first. A field experiment was conducted that had 50 weeds per experimental plot. A standard dose-response experiment was conducted where the weeds were sprayed with different concentrations of the herbicide (in the annoying English units of ounces per gallon). The results were:

Concentration (oz/gallon) Number of dead weeds

0 1

0.010 2

0.030 5

0.10 12

0.30 26

1.0 40

3.0 46

10 49

Calculate the LD₉₅ (in oz/gallon) for this new herbicide.

Question#10: Suppose you are studying a new cholesterol lowering drug. You get approval to conduct a small, exploratory human study. Due to the small number of subjects, you have only 10 people per treatment group. You give all the study participants a cholesterol test at the start to the study to set their baseline values. These are the "pre" values in the table below. The people are then given the test drug for two weeks. One group was given a placebo for a control. Four other groups were given different doses of the drug, namely 10 mg, 50 mg, 100 mg and 150 mg. At the end of the study, all the people are given a cholesterol test to see if the value has dropped. These are the "post" values in the table below. You score anyone having dropped more than 20 points on the cholesterol test as "responding" to the drug.

	Control before treatment	Control after treatment
Subject #1	307	312
Subject #2	271	267
Subject #3	283	285
Subject #4	262	252
Subject #5	232	238
Subject #6	302	289
Subject #7	290	277
Subject #8	285	274
Subject #9	320	317
Subject #10	253	261
	10 mg dose before treatment	10 mg dose after treatment
Subject #1	309	281
Subject #2	287	293
Subject #3	234	223
Subject #4	267	256
Subject #5	289	285
Subject #6	287	261
Subject #7	277	270
Subject #8	318	310
Subject #9	295	287
Subject #10	264	267
	50 mg dose before treatment	50 mg dose after treatment
Subject #1	284	261
Subject #2	312	290
Subject #3	285	273
Subject #4	256	245
Subject #5	307	273
Subject #6	274	268
Subject #7	296	266
Subject #8	288	254
Subject #9	291	278
Subject #10	253	228
	100 mg dose before treatment	100 mg after treatment
Subject #1	283	271
Subject #2	262	233
Subject #3	232	198
Subject #4	285	255
Subject #5	287	271
Subject #6	318	270
Subject #7	302	277
Subject #8	264	238
Subject #9	277	245
Subject #10	290	261
	150 mg dose before treatment	150 mg dose after treatment
Subject #1	288	261
Subject #2	271	244
Subject #3	269	258
Subject #4	302	274
Subject #5	297	267
Subject #6	285	258
Subject #7	298	272
Subject #8	268	237
Subject #9	279	251
Subject #10	280	248

To have this new drug be effective to a wide range of the population, you want the drug to be effective in 87% of the population. Calculate the ED₈₇ for this chemical. You will probably need to extrapolate beyond the range of the dose-response curve.