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Brett is a huge sports fan. He hypothesized half of sports fans liked football the best, 25% liked basketball the best, and 5% liked hockey the best, and the rest liked some other sport the best. He surveyed 500 sports fans and asked what sport they liked the best. Which of the following is the way to calculate the number of these 500 sports fans expected to say that basketball is their favorite sport if the null hypothesis is true?

Answer :

Answer: The goodness-of fit chi square test

Step-by-step explanation:

Using the binomial distribution, it is found that the number of fans expected to say that basketball is their favorite sport is:

[tex]E(X) = np = 500(0.25) = 125[/tex]

For each sports fan, there are only two possible outcomes. Either they like basketball the best, or they do not. The probability of a sport fan liking basketball the best is independent of any other sports fan, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability, and has expected value given by:

[tex]E(X) = np[/tex]

In this problem:

  • 500 sports fans are sampled, hence [tex]n = 500[/tex].
  • A true null hypothesis means that 25% of the fans like basketball the best, hence [tex]p = 0.25[/tex]

Then, the expected number, out of these 500, is:

[tex]E(X) = np = 500(0.25) = 125[/tex]

A similar problem is given at https://brainly.com/question/24261244

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