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Null Hypothesis, significance level, help!

  1. Jul 17, 2011 #1
    1. The problem statement, all variables and given/known data
    You wish to test whether or not a coin is fair, so you toss it 400 times and obtain 225 heads. Test the null hypothesis that the coin is fair and balanced against the alternative that it is not. Use the 5% significance level.
    a.) Identify(using symbols) the null and alternative hypotheses.
    b.) Is this a right tailed, left tailed or two-tailed test?
    c.) Identify the appropriate distribution; give its mean and standard deviation.
    d.) State the formula for the test statistic; substitute the specific values, then calculate the resultant.
    e.) Determine the P-value.
    f.) What is your decision?
    g.) State your conclusion.


    2. Relevant equations
    (work shown below)


    3. The attempt at a solution

    a.) Identify the null and alternative hypotheses.
    Ho: The coin is fair.
    H1: The coin is not fair.

    b.) Is this a right tailed, left tailed or two-tailed test?
    Two tailed test because it may be higher or lower.

    c.) Identify the appropriate distribution; give its mean and standard deviation.
    Normal distribution
    p=.5
    σ= (.5(1-.5))^1/2 / (400)^1/2 = 0.025

    d.) State the formula for the test statistic; substitute the specific values, then calculate the resultant.
    Formula for test statistic: - p / σ
    = 225/400 = 0.5625
    0.5625 - .5 / 0.025 = 2.5

    e.)Determine the P-value.
    P= (1-.9938)2 = 0.0124

    f.) What is your decision?
    P Value(0.0124) is less than the significance level (0.05) so we reject the null hypothesis.

    g.)State your conclusion.
    The coin is not fair.
     
  2. jcsd
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