MathStat474 - HW 11
Posted Nov 5. Due: WED Nov 12.
Remember to always explain your answers.
Problem 1. [this is about conficendce intervals and margin of error]
- What sample size of U.S. adults do you need, if you would like to estimate the proportion of U.S. adults who are “pro-choice” with a 2.5% margin of error (at the 95% level)?
- Your answer to the above question indicates that if you take a
sample of that size, the sample proportion of adults who are pro-choice
is (select one):
- more than 2.5% away from the proportion who are pro-choice among all U.S. adults.
- within 2.5% of the proportion who are pro-choice among all U.S. adults.
- exactly equal to the proportion who are pro-choice among all U.S. adults.
- If you were to use a random sample of size n = 640 U.S. adults
(instead of what you found in question 1), what would the margin of
error roughly be?
- 4%
- .156%
- 3%
- 5%
Problem 2. [problem 9.37 in the book]
A study was conducted to determine if a certain treatment has any effect on the amount of metal removed in a pickling operation. A random sample of 100 pieces was immersed in a bath for 24 hours without the treatment, yielding an average of 12.2 millimeters of metal removed and a sample standard deviation of 1.1 millimeters. A second sample of 200 pieces was exposed to the treatment, followed by the 24-hour immersion in the bath, resulting in an average removal of 9.1 millimeters of metal with a sample standard deviation of 0.9 millimeter. Compute a 98% confidence interval estimate for the difference between the population means. Does the treatment appear to reduce the mean amount of metal removed?
Problem 3. [problem 9.41 in the book]
The following data represent the length of time, in days, to recovery for patients randomly treated with one of two medications to clear up severe bladder infections:
| Medication 1: | Medication 2: | \(\quad\) | \(\quad\) | \(\quad\) | \(\quad\) | \(\quad\) |
|---|---|---|---|---|---|---|
| \(n_1=14\) | \(n_2=16\) | |||||
| \(\bar{x_1}=17\) | \(\bar{x_2}=19\) | |||||
| \(s_1^2=1.5\) | \(s_2^2=1.8\) |
Find a 99% confidence interval for the difference \(\mu_2-\mu_1\) in the mean recovery times for the two medications, assuming normal populations with equal variances.
Problem 4. [problem 9.104 in the book]
Consider Review Exercise 9.103. Let us assume that the data have not been collected yet and that previous statistics suggest that σ1 = σ2 = $4000. Are the sample sizes in Review Exercise 9.103 sufficient to produce a 95% confidence interval on \(\mu_1=\mu_2\) having a width of only $1000? Show all work.
Problem 5 [Extra credit]
Choose either problem 9.81 or 9.85 from the book:
9.81. asks for an MLE for \(p\) in a Bernoulli process; 9.85 asks for an MLE for \(\theta\) in a uniform distribution.
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