Statistics homework help. STAT 3300 Homework #4
Due Wednesday, 05/19/2020
Note: Answer these questions on a separate piece of paper. In the top right corner, include
your name, SMU ID, and course number. Please include a title for the assignment so that
it is clear to the graders. If you miss class the day the assignment is turned in, submit this
before class in order to receive credit.
Question 1 (25 points total)
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 rejected.
a) (5 points) Find the proportion of rejects for each age group.
b) (10 points) Find a 99% confidence interval for the difference in the proportions.
c) (10 points) Use a significance test to compare the proportions. Write a short paragraph describing your
results and conclusions.
Question 2 (10 points total)
Young children need calcium in their diet to support the growth of their bones. The Institute of Medicine
provides guidelines for how much calcium should be consumed by people of different ages. One study examined
whether or not a sample of children consumed an adequate amount of calcium based on these guidelines.
Because there are different guidelines for children aged 5 to 10 years and those aged 11 to 13 years, the
children were classified into these two age groups. Each student’s calcium intake was classified as meeting or
not meeting the guideline. There were 2029 children in the study. Here are the data:
Met Requirement Age (5-10 years) Age (11 to 13 years)
No 194 557
Yes 861 417
Identify the populations, the counts, and the sample sizes for comparing the extent to wich the two age
groups of children met the calcium intake requirement.
Question 3 (10 points total)
Refer to the previous question. Use a 95% confidence interval for the comparison and explain what the
confidence interval tells us. Be sure to include a justification for the use of the large-sample procedure for
this comparison.
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Question 4 (10 points total)
Again, refer to question 2. Use a significance test to make the comparison. Interpret the result of your test.
Be sure to include a justification for the use of the large-sample procedure for this comparison.
Question 5 (15 points total)
A major court case on the health effects of drinking contaminated water took place in the town of Woburn,
Massachusetts. A town well in Woburn was contaminated by industrial chemicals. During the period that
residents drank water from this well, there were 16 birth defects among 414 births. In years when the
contaminated well was shut off and water was supplied from other wells, there were three birth defects among
228 births. The plaintiffs suing the firm responsible for the contamination claimed that these data show that
the rate of birth defects was higher when the contaminated well was in use. How statistically significant is the
evidence? What assumptions does your analysis require? Do these assumptions seem reasonable in this case?
Question 6 (10 points)
You want to know which of two manufacturing processes will be better. From a previous student, we believe
the defective proportion in the first process to be somewhere around 0.1 and the defective proportion in the
second process to be around 0.15. To compare the defective proportions between the two manufacturing
processes, we plan to construct a 90% confidence interval that will have a margin of error of 0.05 or less.
What would we choose for our sample size?
Question 7 (10 points)
You want to compare two manufacturing processes. From a previous student, we believe the defective
proportion in the first process to be somewhere around 0.1 and the defective proportion in the second process
to be around 0.15. We want to know whether the defective rates are different between the two manufacturing
processes. We desire a power of at least 80% and a 10% significance level. How many products do we need in
each group to run this experiment within these parameters?
Question 8 (10 points)
In the previous question, all other things being the same, what is the sample size needed if we want to know
whether the defective rate from the first process is smaller than that from the second manufacturing process?
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