Use the Excel output to write out the conclusions of the Two-way Anova F-test, and use a 5% significance level. Choose the options that would create the correct row factor hypotheses. Ho: [ Select ] ["Poisons", "Medications", "Survival Times"] [ Select ] ["do not depend on", "depend on"]
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Use the Excel output to write out the conclusions of the Two-way Anova F-test, and use a 5% significance level.
Choose the options that would create the correct row factor hypotheses.
Ho: [ Select ] ["Poisons", "Medications", "Survival Times"] [ Select ] ["do not depend on", "depend on"] [ Select ] ["Poisons", "Survival Times", "Medications"] .
Ha: [ Select ] ["Medications", "Survival Times", "Poisons"] [ Select ] ["do not depend on", "depend on"] [ Select ] ["Poisons", "Medications", "Survival Times"] .
![Data from "Statistics For Experimenters" by Box Hunter Hunter, 1978.
The data “... appear in a paper by Box and Cox (1964). These are survival
times of groups of four animals randomly allocated to three poisons and four
treatments. The experiment was part of an investigation to combat the
effects of certain toxic agents. This arrangement is called a 3 x 4 factorial
design and is replicated four times."
The aim here is to see how the different poisons and medications affect
survival times. Survival time is measured in ten-hours.
Use the information provided below to answer the SURVIVAL TIMES
questions that follow.
Two-way Anova: SURVIVAL TIMES (DATA)
MEDICATIONS
D
Means
0.31
0.82
0.43
0.45
0.45
1.1
0.45
0.71
0.6175
0.46
0.88
0.63
0.66
0.43
0.72
0.76
0.62
0.36
0.92
0.44
0.56
0.29
0.61
0.35
1.02
II
0.5444
0.4
0.49
0.31
0.71
0.23
1.24
0.4
0.38
0.22
0.3
0.23
0.3
0.21
0.37
0.25
0.36
II
0.2763
0.18
0.38
0.24
0.31
0.23
0.29
0.22
0.33
Means
0.3142
0.6767
0.3925
0.5342
0.4794
SNOSIOD](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67cd3f4f-dcc4-44d4-83f4-13332296f2a9%2Fe4676f53-ae22-4e35-a589-35c8ea99a215%2Fz7wpuj8_processed.png&w=3840&q=75)
![Two-way Anova: SURVIVAL TIMES (EXCEL OUTPUT)
Anova: Two-Factor
SUMMARY
A
B
Total
Count
4
4
4
4
16
Sum
1.65
3.52
2.27
2.44
9.88
Average
0.4125
0.88
0.5675
0.61
0.6175
Variance
0.004825
0.02586667 0.02455833
0.01273333
0.04386
Count
4
4
4
4
16
Sum
1.28
3.26
1.5
2.67
8.71
Average
0.32
0.815
0.375
0.6675
0.544375
Variance
0.00566667
0.1131
0.00323333
0.073425
0.08373292
Count
4
4
4
16
Sum
0.84
1.34
0.94
1.3
4.42
Average
0.21
0.335
0.235
0.325
0.27625
Variance
0.00046667 0.00216667 0.00016667
0.0007
0.00387833
Total
Count
12
12
12
12
Sum
3.77
8.12
4.71
6.41
Average
0.31416667 0.67666667
0.3925
0.53416667
Variance
0.01046288 0.10293333 0.02789318
0.04815379
ANOVA
Source of Variation
S
df
MS
F
P-value
F crit
Sample
1.0330125
0.51650625
2
23.2217366
3.3314E-07
3.259446306
Columns
0.92120625
3
0.30706875
13.8055824
3.7773E-06
2.866265557
Interaction
0.2501375
0.04168958
1.87433264
0.11225061
2.363750958
Within
0.800725
36
0.02224236
Total
3.00508125
47](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67cd3f4f-dcc4-44d4-83f4-13332296f2a9%2Fe4676f53-ae22-4e35-a589-35c8ea99a215%2F8t8wjwi_processed.png&w=3840&q=75)
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