Baseball fans marvel at the home runs Willie Mays Hayes (from the movie “Major League”!) hits. To get an idea of how far his home runs travel, a random sample of 6 home runs is used. The distance of each home run in the sample is given below: {440, 460, 420, 470, 460, 450} a. Assuming home run distances are normally distributed (so the Central Limit Theorem applies), construct a 95% confidence interval for the mean home run distance. b. A number of teams are interested in acquiring Hayes for their teams. In particular, the Baltimore Orioles are seriously interested in pursuing him to bolster their sagging offense. The manager of the Orioles thinks that the stadium in Baltimore, Camden Yards, would hurt Hayes’s home run production. He estimates that Hayes would need to average better than 430 ft per home run to maintain his home run production in Camden Yards. Is there sufficient evidence at the level to put the manager’s mind at α =.05 ease? (use the p value approach)
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
Baseball fans marvel at the home runs Willie Mays Hayes (from the movie “Major League”!) hits. To get an idea of how far his home runs travel, a random sample of 6 home runs is used. The distance of each home run in the sample is given below: {440, 460, 420, 470, 460, 450}
a. Assuming home run distances are
b. A number of teams are interested in acquiring Hayes for their teams. In particular, the Baltimore Orioles are seriously interested in pursuing him to bolster their sagging offense. The manager of the Orioles thinks that the stadium in Baltimore, Camden Yards, would hurt Hayes’s home run production. He estimates that Hayes would need to average better than 430 ft per home run to maintain his home run production in Camden Yards. Is there sufficient evidence at the level to put the manager’s mind at α =.05 ease? (use the p value approach)
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