Question

The article "Poll Finds Most Oppose Return to Draft, Wouldn't Encourage Children to Enlist" (Associated Press, December 18,2005 ) reports that in a random sample of 1,000 American adults, 430 answered yes to the following question: "If the military draft were reinstated, would you favor drafting women as well as men?" The data were used to test \(H_{0}: p=0.5\) versus \(H_{i}: p<0.5,\) and the null hypothesis was rejected. (Hint: See discussion at bottom of page 426\()\) a. Based on the result of the hypothesis test, what can you conclude about the proportion of American adults who favor drafting women if a military draft were reinstated? b. Is it reasonable to say that the data provide strong support for the alternative hypothesis? c. Is it reasonable to say that the data provide strong evidence against the null hypothesis?

Short answer

The result of the hypothesis test suggests that less than 50% of American adults favor drafting women if a military draft were reinstated. It's reasonable to say that the data provides some degree of support for the alternative hypothesis and evidence against the null hypothesis, but without the p-value, the strength of this support and evidence can't be clarified.

Step-by-step solution

Identify the sample proportion

From the exercise, we know 430 out of the 1000 adults sampled answered 'yes'. This gives a sample proportion, \(p' = \frac{430}{1000}\)

Conduct a hypotheses test

Using the sample proportion, \(p'\), and the given hypotheses \(H_{0}: p=0.5\) versus \(H_{i}: p<0.5\), conduct a hypotheses test. The null hypothesis, representing 50% support for drafting women, is rejected based on this test.

Interpret the findings

The rejection of the null hypothesis implies that the proportion of adults favoring the drafting of women is less than 0.5

Discuss the Support for the Alternative Hypothesis

Given that the null hypothesis is rejected, it can be stated that the data supports the alternative hypothesis to some degree. However, referring to it as 'strong support' cannot be concluded from the information provided. We need to know the p-value to discuss how strong that support is.

Discuss the evidence against the Null Hypothesis

The evidence against the null hypothesis is the rejection of it. This implicates that the proportion of those in favor of drafting women is less than 0.5. However, just as with the alternative hypothesis, the strength of this evidence can only be determined by analyzing the p-value which has not been provided in this problem.