Question 1085931: Suppose that you take a random sample of 10,000 Americans and find that 1,111 are left- handed. You perform a test of significance to assess whether the sample data provide evidence that more than 10% of all Americans are left handed, and you calculate a test statistic of 3.70 and a p-value of .0001. Furthermore, you calculate a 99% confidence interval for the proportion of lefthanders in America to be (.103,.119). Consider the following statements: The sample provides strong evidence that more than 10% of all Americans are left handed. The sample provides evidence that the proportion of left-handers in America is much larger than 10%. Which of these two statements is the more appropriate conclusion to draw? Explain your answer based on the results of the significance test and confidence interval.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! We have two statements
Statement A: The sample provides strong evidence that more than 10% of all Americans are left handed
Statement B: The sample provides evidence that the proportion of left-handers in America is much larger than 10%
They basically say the same thing, but the qualifier for statement B is much more extreme. Because the p value is so very small (0.0001), this means that the event of the null distribution being correct is very very unlikely. Therefore, we strongly reject the null indicating that the proportion of left handers is likely to be much larger than 10%. If we got a p value closer to 0.01 or 0.05, then we still might reject H0 but not as strongly. So because of the very small p value, we should go with statement B.
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