Suppose that you take a random sample of 10000 Americans and

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 left-handers 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.

Solution

Consider the following statements:

The sample provides strong evidence that more than 10% of all Americans are left-handed. [ANSWER, MORE APPROPRIATE]

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We do not use \"much larger\" because the lower bound of the confidence interval actually is close to 0.1 (actually, even the upper bound).

As the P value is 0.0001, very small, then this is a strong evidence.

Thus, this is the more appropriate of the two.