Researchers presented chimpanzee subjects with food outside their cage that they could bring within reach by pulling two ropes, one attached to each end of the food tray. If a chimp pulled only one rope, the rope came loose and the food was lost. Another chimp was available as a partner, but only if the subject unlocked a door joining two cages. The same eight chimpanzee subjects faced this problem in two versions: the two ropes were close enough together that one chimp could pull both (no collaboration needed), or the two ropes were too far apart for one chimp to pull both (collaboration needed). The data shows how often in 24 trials for each version each subject opened the door to recruit another chimp as partner. (a) Is there evidence that chimpanzees recruit partners more often when a problem requires collaboration? Hint: Let m be the mean difference (collaboration required minus not) in the number of times a subject recruited a partner. The null hypothesis is that the need for collaboration has no effect on how often partners are recruited.
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.
Researchers presented chimpanzee subjects with food outside their cage that they could bring within reach by pulling two ropes, one attached to each end of the food tray. If a chimp pulled only one rope, the rope came loose and the food was lost. Another chimp was available as a partner, but only if the subject unlocked a door joining two cages. The same eight
chimpanzee subjects faced this problem in two versions: the two ropes were close enough together that one chimp could pull both (no collaboration needed), or the two ropes were too far apart for one chimp to pull both (collaboration needed). The data shows how often in 24 trials for each version each subject opened the door to recruit another chimp as partner.
(a) Is there evidence that chimpanzees recruit partners more often when a problem requires collaboration?
Hint: Let m be the mean difference (collaboration required minus not) in the number of times a subject recruited a
partner. The null hypothesis is that the need for collaboration has no effect on how often partners are recruited.
(b) Find a 95% confidence interval for the mean difference (collaboration required minus not) in the number
of times a subject recruited a partner.
| Chimpanzee | Collaboration Needed YES | Collaboration Needed NO | Differences Yes - No |
| Namuiska | 16 | 0 | 16 |
| Kalema | 16 | 1 | 15 |
| Okech | 23 | 5 | 18 |
| Baluku | 19 | 3 | 16 |
| Umugenzi | 15 | 4 | 11 |
| Indi | 20 | 9 | 11 |
| Bili | 24 | 16 | 8 |
| Asega | 24 | 20 | 4 |
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