An educational psychologist is studying two methods of tutoring young children: Method A and Method B. She wants to test whether there is any difference in puzzle solving skills between children tutored by one method versus children tutored by the other. Independent samples of 13 children who were tutored using Method A and 10 children who were tutored using Method B were chosen at random. The Method A children took a mean of 31 minutes to solve a certain puzzle with a standard deviation of 3 minutes. The Method B children took a mean of 36 minutes to solve the same puzzle with a standard deviation of 7 minutes. Assume that the two populations of completion times are normally distributed and that the population varlances are equal. Construct a 95% confidence interval for the difference H between the mean puzzle-solving times for Method A children (4,) and for Method B children (u). Then find the lower limit and upper limit of the 95% confidence interyal. Carry your intermediate computations to at least three decimal places. Round your responses to at least two decimal places. (If necessary, consult a list of formulas.) Lower limit: ] x 5 ? Upper limit:
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.
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