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22 February, 01:26

A sports writer hypothesized that Tiger Woods plays better on par 3 holes than on par 4 holes. He reviewed Woods' performance in a random sample of golf tournaments. On the par 3 holes, Woods made a birdie in 20 out of 80 attempts. On the par 4 holes, he made a birdie in 40 out of 200 attempts. How would you interpret this result?

a. The p-value is < 0.001, very strong evidence that Woods plays better on par 3 holes.

b. The p-value is between 0.001 and 0.01, strong evidence that Woods plays better on par 3 holes.

c. The p-value is between 0.01 and 0.05, moderate evidence that Woods plays better on par 3 holes.

d. The p-value is between 0.05 and 0.1, some evidence that Woods plays better on par 3 holes.

e. The p-value is > 0.1, little or no support for the notion that Woods plays better on par 3 holes.

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  1. 22 February, 01:39
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    e. The p-value is > 0.1, little or no support for the notion that Woods plays better on par 3 holes.

    Step-by-step explanation:

    Hypothesis by the sports writer

    On the par 3 holes, Tiger Woods made a birdie in 20 out of 80 attempts. On the par 4 holes, he made a birdie in 40 out of 200 attempts.

    Null hypothesis: P 3 < = P 4

    Alternative hypothesis: P 3 > P 4

    Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the proportion of birdies on par 3 holes (p 3) is sufficiently greater than the proportion of birdies on par 4 holes (p 4)

    Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).

    p = (p3 * n 3 + p4 * n4) / (n3 + n) = [ (0.25 * 80) + (0.20 * 200) ] / (80 + 200) = 50/280 = 0.214

    SE = sqrt{ p * (1 - p) * [ (1/n3) + (1/n4) ] }

    SE = sqrt [ 0.214 * 0.786 * (1/80 + 1/200) ]

    = sqrt[ 0.214 * 0.786 * 0.0175 }

    = sqrt [0.0029548] = 0.0544

    z = (p3 - p4) / SE = (0.25 - 0.20) / 0.0544 = 0.92

    where p3 is the sample proportion of birdies on par 3,

    p4 is the sample proportion of birdies on par 4,

    n3 is the number of par 3 holes,

    and n4 is the number of par 4 holes.

    Since we have a one-tailed test, the P-value is the probability that the z-score is greater than 0.92. We use the Normal Distribution Calculator to find P (z > 0.92) = 0.18. Thus, the P-value = 0.18.

    Since the P-value (0.18) is greater than 0.10, we have little support for the notion that Woods plays better on par 3 holes. In short, we cannot reject the null hypothesis
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