Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 486 five-syllable sequences from this manuscript showed that 127 were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato's Symposium? Use α = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. A. H0: p > 0.214; H1: p = 0.214 B. H0: p < 0.214; H1: p = 0.214 C. H0: p = 0.214; H1: p < 0.214 D. H0: p = 0.214; H1: p ≠ 0.214 E. H0: p = 0.214; H1: p > 0.214 (b) What sampling distribution will you use? The standard normal, since np < 5 and nq < 5.The Student's t, since np > 5 and nq > 5. The Student's t, since np < 5 and nq < 5.The standard normal, since np > 5 and nq > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value of the test statistic. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.
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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