Lab Project
Problem 1
Of the last ten times you've dropped your toast, it landed sticky-side down nine times. If these are a random sample from the $\text{Ber}(p)$ distribution, find an 80% confidence interval for $p$, the probability of the stidy side landing down. (Use `binconf()`
Problem 2
A survey is taken of 250 students, and a $\hat{p}$ of 0.45 is found. The same survey is repeated with 1000 students, and the same $\hat{p}$ is found. Compare the two 95% confidence intervals. What is the relationship? Is the margin of error for the second one four times smaller? If not, how much smaller is it? (Use `binom.test()` to answer this problem.)
Problem 3
For the `Melanoma` (**MASS**) data set, use `prop.test()` to find a 99% confidence interval for the difference in proportion of male and female patients with an ulcer.
Problem 4
The `tud.recs` (**UsingR**) data set contains a sample of math SAT scores from some population in the variable `sat.m`. Find a 90% confidence interval for the mean math SAT score for this data. (Do not use `t.test(); find this confidence interval "by hand".)
Problem 5
For the `homedata` (**UsingR**) data set find 90% confidence intervals for both variables `y1970` and `y2000`, assuming the sample represents some population. Use `t.test()`, but first discuss whether the model assumptions are appropriate (include some check of the assumptions, like a Q-Q plot).
Problem 6
In determining the recommended dosage of AZT for AIDS patients, tests were done comparing efficacy for various dosages. If a low dosage is effective, then that would be recommended, as it would be less expensive and would have fewer potential side effects.
A test to decide whether a dosage of 1,200 mg is similar to one of 400 mg is performed on two random samples of AIDS patients. A numeric measurement of a patient's health is made, and the before-and-after differences are recorded after treatment:
|Treatment | | | | | | | | | | |
|--------------:|---|---|---|---|----|----|----|---|---|---|
| 400 mg group | 7 | 0 | 8 | 1 | 10 | 12 | 2 | 9 | 5 | 2 |
| 1200 mg group | 2 | 1 | 5 | 1 | 5 | 7 | -1 | 8 | 7 | 3 |
Find a 90% confidence interval for the differences of the means. What do you assume about the data?
Problem 7
The following data is from IQ tests for pairs of twins that were separated at birth. One twin was raised by the biological parents, the other by adoptive parents.
| Twin pair | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|-----------:|----|----|----|-----|----|----|----|----|-----|-----|
| Foster | 80 | 88 | 75 | 113 | 95 | 82 | 97 | 94 | 132 | 108 |
| Biological | 90 | 91 | 79 | 97 | 97 | 82 | 87 | 94 | 131 | 115 |
Find a 90% confidence interval for the differences of mean. What do you assume about the data? In particular, are the two samples independent?