Suppose that you take a random sample of 10,000 Americans and find that 1,111 ar

Question

Suppose that you take a random sample of 10,000 Americans and find that 1,111 are left-handed. You perform a test if 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 3070 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.

Explanation / Answer

The null and alternative hypothesis are,

Ho : P = 10% = 0.1

Ha: P > 0.1

The P value is 0.0001 which is very small theirfore we reject Ho at any significance level (1%,25,5%,10%)

sample data provide evidence that more than 10% of all Americans are left-handed.

99 % confidence interval for proportion of left handers in America is,

( 0.103 , 0.119)

There is 99 % chance that our proportion of left handed (10%) lies in this confidence interval.

Theirfore the statment ,

The sample provides strong evidence that more than 10% of all Americans are left-handed is more appropriate to draw conclusion.

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