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Teeth and military service. In 1898 the United States and
Chapter , Problem 8.58(choose chapter or problem)
Teeth and military service. In 1898 the United States and Spain fought a war over the U.S. intervention in the Cuban War of Independence. At that time the U.S. military was concerned about the nutrition of its recruits. Many did not have a sufficient number of teeth to chew the food provided to soldiers. As a result, it was likely that they would be undernourished and unable to fulfill their duties as soldiers. The requirements at that time specified that a recruit must have “at least four sound double teeth, one above and one below on each side of the mouth, and so opposed” so that they could chew food. Of the 58,952 recruits who were under the age of 20,68 were rejected for this reason. For the 43,786 recruits who were 40 or over, 3801 were \(\text { rejected. }{ }^{19}\)
(a) Find the proportion of rejects for each age group.
(b) Find a 99% confidence interval for the difference in the proportions.
(c) Use a significance test to compare the proportions. Write a short paragraph describing your results and conclusions.
(d) Are the guidelines for the use of the large-sample approach satisfied for your work in parts (b) and (c)? Explain your answers.
Questions & Answers
QUESTION:
Teeth and military service. In 1898 the United States and Spain fought a war over the U.S. intervention in the Cuban War of Independence. At that time the U.S. military was concerned about the nutrition of its recruits. Many did not have a sufficient number of teeth to chew the food provided to soldiers. As a result, it was likely that they would be undernourished and unable to fulfill their duties as soldiers. The requirements at that time specified that a recruit must have “at least four sound double teeth, one above and one below on each side of the mouth, and so opposed” so that they could chew food. Of the 58,952 recruits who were under the age of 20,68 were rejected for this reason. For the 43,786 recruits who were 40 or over, 3801 were \(\text { rejected. }{ }^{19}\)
(a) Find the proportion of rejects for each age group.
(b) Find a 99% confidence interval for the difference in the proportions.
(c) Use a significance test to compare the proportions. Write a short paragraph describing your results and conclusions.
(d) Are the guidelines for the use of the large-sample approach satisfied for your work in parts (b) and (c)? Explain your answers.
ANSWER:Step 1 of 5
Given: The sample number of recruits who were under the age of 20 is \(n_{1}=58952\)
The sample number of recruits who were 40 or over is \(n_{2}=43786\)
The number of recruits under the age of 20 who were rejected is \(X_{1}=68\)
The number of recruits who were 40 or over and were rejected is \(X_{2}=3801\)