Statistics with R
Student Resources
Chapter 9: Hypothesis Tests: Introduction, Basic Concepts, and an Example
1. A triangle taste test consists of 11 identical trials on which the subject attempts to identify the odd sample on each trial. Assume that there are 2 possible rejection regions: RR7 = {7, 8, 9, 10, 11} and RR9 = {9, 10, 11}. Assuming that the rejection region is RR7 = {7, 8, 9, 10, 11}, what is the probability of Type I error, α?
- 0.03862894 X
- 0.00743508
- 0.03725719
- 0.00194642
Solution:
> 1 - pbinom(6, 11, 1/3)
[1] 0.03862894
or
> sum(dbinom(7 : 11, 11, 1/3))
[1] 0.03862894
2. With a rejection region of RR7 = {7, 8, 9, 10, 11}, what is the probability of a Type II error, β, if the subject has a probability of p=2/3 of identifying the odd sample?
- 0.0073307
- 0.2503683
- 0.2889973 X
- 0.2754052
Solution:
> pbinom(6, 11, 2/3)
[1] 0.2889973
or
> sum(dbinom(0 : 6, 11, 2/3))
[1] 0.2889973
3. With a rejection region of RR9 = {9, 10, 11}, what is the probability of Type I error, α?
- 0.002567901
- 0.001975309
- 0.001646091
- 0.001371742 X
Solution:
> 1 - pbinom(8, 11, 1/3)
[1] 0.001371742
or
> sum(dbinom(9 : 11, 11, 1/3))
[1] 0.001371742
4. With a rejection region of RR9 = {9, 10, 11}, what is the probability of a Type II error, β, if the subject has a probability of p=2/3 of identifying the odd sample?
- 0.7658893 X
- 0.5744170
- 0.8424783
- 0.7275949
Solution:
> pbinom(8, 11, 2/3)
[1] 0.7658893
or
> sum(dbinom(0 : 8, 11, 2/3))
[1] 0.7658893
5. What is the p-value for a subject who achieves x = 9 correct identifications in n=11 trials?
- 0.002057613
- 0.001371742 X
- 0.003429355
- 0.001097394
Solution:
> 1 - pbinom(8, 11, 1/3)
[1] 0.001371742
or
> sum(dbinom(9 : 11, 11, 1/3))
[1] 0.001371742
6. Another triangle taste test consists of 16 identical trials on which the subject attempts to identify the odd sample on each trial. Assume that there are 2 possible rejection regions: RR10 = {10, 11, 12, 13, 14, 15, 16} and RR12 = {12, 13, 14, 15, 16}. With a rejection region of RR10 = {10, 11, 12, 13, 14, 15, 16}, what is the probability of Type I error, α?
- 0.00403954
- 0.04996248
- 0.12650070
- 0.01594549 X
Solution:
> 1 - pbinom(9, 16, 1/3)
[1] 0.01594549
or
> sum(dbinom(10 : 16, 16, 1/3))
[1] 0.01594549
7. With a rejection region of RR10 = {10, 11, 12, 13, 14, 15, 16}, what is the probability of a Type II error, β, if the subject has a probability of p=0.75 of identifying the odd sample?
- 0.17531340
- 0.07955725 X
- 0.15940540
- 0.02665733
Solution:
> pbinom(9, 16, 0.75)
[1] 0.07955725
or
> sum(dbinom(0 : 9, 16, 0.75))
[1] 0.07955725
8. With a rejection region of RR12 = {12, 13, 14, 15, 16}, what is the probability of Type I error, α?
- 0.0007924645 X
- 0.0040395410
- 0.0001159903
- 0.0159454900
Solution:
> 1 - pbinom(11, 16, 1/3)
[1] 0.0007924645
or
> sum(dbinom(12 : 16, 16, 1/3))
[1] 0.0007924645
9. With a rejection region of RR12 = {12, 13, 14, 15, 16}, what is the probability of a Type II error, β, if the subject has a probability of p=0.75 of identifying the odd sample?
- 0.1896546
- 0.5500959
- 0.3698138 X
- 0.2017546
Solution:
> pbinom(11, 16, 0.75)
[1] 0.3698138
or
> sum(dbinom(0 : 11, 16, 0.75))
[1] 0.3698138
10. What is the p-value for a subject who achieves x = 11 correct identifications in n=16 trials?
- 0.049962480
- 0.015945490
- 0.000792464
- 0.004039541 X
Solution:
> 1 - pbinom(10, 16, 1/3)
[1] 0.004039541
> sum(dbinom(11 : 16, 16, 1/3))
[1] 0.004039541