A poll taken by the Software Usability Research Laboratory surveyed 341 video gamers, and found 110 of them said that they prefer playing games on a console, rather than a computer or hand-held device. An executive at a game console manufacturing company claims that more than 25% of gamers prefer consoles. Does the poll provide convincing evidence that the claim is true? Use the α=0.05 level of significance. a) State the null and alternative hypotheses. b) What statistical test should you use to test your hypotheses (hint: which function on your calculator do you need to test) c) Using your calculator, test your hypotheses. What is the pvalue? d) Using the decision rule, would you reject or not reject the null hypotheses? Explain why. e) What would you conclude regarding the executive's claim? f) If there was a mistake, what type of error would the researchers make?
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.
A poll taken by the Software Usability Research Laboratory surveyed 341 video gamers, and found 110 of them said that they prefer playing games on a console, rather than a computer or hand-held device. An executive at a game console manufacturing company claims that more than 25% of gamers prefer consoles. Does the poll provide convincing evidence that the claim is true? Use the α=0.05 level of significance.
a) State the null and alternative hypotheses.
b) What statistical test should you use to test your hypotheses (hint: which
c) Using your calculator, test your hypotheses. What is the pvalue?
d) Using the decision rule, would you reject or not reject the null hypotheses? Explain why.
e) What would you conclude regarding the executive's claim?
f) If there was a mistake, what type of error would the researchers make?
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