An advertising agency won’t sign an athlete for product endorsement unless it is sure that the athlete is recognised by more than 25% of its target audience. The agency always conducts a poll to investigate the level of recognition of the athlete before offering a contract. (a) What sample size for the poll should the agency use if it wants to be 90% sure that the proportion of the sample who recognise an athlete will be within 0.03 of the true proportion for its target audience? (b) The target audience for a new sports deodorant is 13 to 19 year-old girls who play sport. From a sample of 800 teenagers from this population a total of 216 indicated that they recognised a particular Olympic swimmer. What are the population and random variable under consideration in this case? (c) Calculate a 95% confidence interval for the population level of recognition for this swimmer. Be sure to outline any necessary conditions for validity of this confid
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.
An advertising agency won’t sign an athlete for product endorsement unless it is sure that the athlete is recognised by more than 25% of its target audience. The agency always conducts a poll to investigate the level of recognition of the athlete before offering a contract.
(a) What
(b) The target audience for a new sports deodorant is 13 to 19 year-old girls who play sport. From a sample of 800 teenagers from this population a total of 216 indicated that they recognised a particular Olympic swimmer. What are the population and random variable under consideration in this case?
(c) Calculate a 95% confidence interval for the population level of recognition for this swimmer. Be sure to outline any necessary conditions for validity of this confidence interval.
(d) Will this Olympic swimmer be offered a contract to endorse the sports deodorant by the advertising agency? Use the confidence interval from (c) in your reasoning.
(e) A tennis player has recognition rate of 70% in the general population. What is the probability that less than 65% of a random sample of 420 people would recognise this tennis player?
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