Null hypothesis, alternative hypothesis, statistics!

  1. 1. The problem statement, all variables and given/known data
    Assume that the cholesterol level of college aged men nationwide is normally distributed with mean of 180 and standard deviation is 20. Twelve male MVCC students were randomly selected; the cholesterol level of each was determined: 250, 220, 145, 225, 170, 210, 200, 210, 130, 210, 180 and 190. Is there evidence (at the 1% significance level) that the average male MVCC student has higher cholesterol level than the general population?
    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: There is no evidence that the average male MVCC student has higher cholesterol level than the general population.
    H1: There is evidence that the average male MVCC student has higher cholesterol level than the general population.

    b.) Is this a right tailed, left tailed or two-tailed test?
    Right tailed test because the average male MVCC student has higher cholesterol than the general population.

    c.)Identify the appropriate distribution; give its mean and standard deviation.
    The distribution of the sample distribution is roughly symmetric with a slight right skew. The mean is 195 and the σ is 34.17.

    d.)State the formula for the test statistic; substitute the specific values, then calculate the resultant.
    Formula: (x bar - p)/ σ
    = 250+220+145+225+170+210+200+210+130+210+130+210+180+190= 2340/12 = 195
    (195-180)/5.7735 = 2.5981

    e.) Determine the P-value:
    P=1-0.9952=0.00469

    f.) What is your decision?
    P value(0.0048) is less than significance level (.01) therefore I reject the null hypothesis.

    g.)State your conclusion.
    Because we reject our null hypothesis our conclusion is there is evidence that the average male MVCC student has higher cholesterol level than the general population. The probability that this conclusion was drawn due to random variation is 0.00469.
     
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