Difference between statistic and null hypothesis parameter value 6. A second fac

Question

Difference between statistic and null hypothesis parameter value 6. A second factor that influences the strength of evidence against the null is how far apart the observed sample statistic and the value of the parameter specified under the null hypothesis are. For this study the null value was 0.50 and the observed sample statistic was about 0.543 (or 54.3% of the competitors wearing red won their matches). Suppose a larger proportion of competitors wearing red won their matches. If fact, suppose 57% of the 457 matches were won by a competitor wearing red a. Go back to the One Proportion applet and approximate the (one-sided) p-value for this situation where again we are testing to see whether the overll probablity of winning is more than 0.50. b. Is your p-value larger or smaller than your original onet Explain why this makes sense. o. Write a sentence explaining the relationship between the distance between the observed sample statistic and the value of the parameter specified under the null hypothesis to the strength of evidence against the null hypothesis

Explanation / Answer

a.
Test statistics, z, when sample statistics was 0.57
z = (0.57 - 0.5)/sqrt(0.5*0.5/457) = 2.9929

p-value = 0.0014

b.
p-value is less than original one.
This is because the value of test statistics calculated for sample statistics 0.57 is greater than the value of test statistics calculated for sample statistics 0.543.

Higher the value of z in the right tail, lower the value of area to the value of z which indicates the p-value.

c.
We can generalize the observation as "Higher the distance between the observed sample statistics and the value of the parameter specified under the null hypothesis, higher the strength of the evidence against the null hypothesis"

This is because if p-value goes below the significance level, we reject the null hypothesis.

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