Do Babies Understand Probability?Can babies reason probabilistically? A study1 investigates this by showing ten- to twelve-month-old infants two jars of lollipop shaped objects colored pink or black. Each infant first crawled or walked to whichever color they wanted, determining their “preferred” color. They were then given the choice between two jars that had the same number of preferred objects, but that differed in their probability of getting the preferred color; each jar had 12 in the preferred color and either 4 or 36 in the other color. Babies choosing randomly or based on the absolute number of their preferred color would choose equally between the two jars, while babies understanding probability would more often choose the jar with the higher proportion of their preferred color. Of the 24 infants studied, 18 chose the jar with the higher proportion of their preferred color. Are infants more likely to choose the jar with the higher proportion of their preferred color? a) State the null and alternative hypotheses. b) Give the notation for the sample statistic. c) Find the value of the sample statistic. Round your answer to two decimal places.
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.
Do Babies Understand
Can babies reason probabilistically? A study1 investigates this by showing ten- to twelve-month-old infants two jars of lollipop shaped objects colored pink or black. Each infant first crawled or walked to whichever color they wanted, determining their “preferred” color. They were then given the choice between two jars that had the same number of preferred objects, but that differed in their probability of getting the preferred color; each jar had 12 in the preferred color and either 4 or 36 in the other color. Babies choosing randomly or based on the absolute number of their preferred color would choose equally between the two jars, while babies understanding probability would more often choose the jar with the higher proportion of their preferred color. Of the 24 infants studied, 18 chose the jar with the higher proportion of their preferred color. Are infants more likely to choose the jar with the higher proportion of their preferred color?
a) State the null and alternative hypotheses.
b) Give the notation for the sample statistic.
c) Find the value of the sample statistic. Round your answer to two decimal places.
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