Statistics

The International Olympic Committee states that the female participation in the 2000 Summer Olympic Games was 42%, even with new sports such as weight lifting, hammer throw, and modern pentathlon being added to the Games. Broadcasting and clothing companies want to change their advertising and marketing strategies if the female participation increases at the next games. An independent sports expert arranged for a random sample of pre-Olympic exhibitions. The sports expert reported that 202 of 454 athletes in the random sample were women. Is this strong evidence that the participation rate may increase? Test an appropriate hypothesis and state your conclusion.

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  1. Let's set up the null and alternative hypothesis, find a formula to use, then go from there.

    Null hypothesis:
    Ho: p = .42 -->meaning: population proportion is equal to .42
    Alternative hypothesis:
    Ha: p > .42 -->meaning: population proportion is greater than .42

    [ Note: The null hypothesis is what we suspect isn't true, while the alternative hypothesis is what we suspect is true (or claim to be true). The null hypothesis ALWAYS uses an equals sign. ]

    Using a formula for a binomial proportion one-sample z-test with your data included, we have:
    z = .44 - .42 -->test value (202/454 = .44) minus population value (.42)
    divided by √[(.42)(.58)/454] -->.42 represents 42%, .58 represents 1-.42, and 454 is the sample size.

    Finish the calculation and draw your conclusions. Remember if you reject the null and accept the alternative hypothesis, you will have determined there is enough evidence to support the claim that the participation rate has increased. If the null is not rejected, you cannot conclude a difference.

    I hope this will help.

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