1. Which is wider, a 95% or a 99% confidence interval?
2. When you construct a 95% confidence interval, what are you 95% confident about?
3. When computing a confidence interval, when do you use t and when do you use z?
4. Assume a researcher found that the correlation between a test he or she developed and job performance was .5 in a study of 25 employees. If correlations under .30 are considered unacceptable, would you have any reservations about using this test to screen job applicants?
5. What is the effect of sample size on the width of a confidence interval?
6. How might an experimenter demonstrate that a drug has a negligible effect?
7. When is Fisher's z' used? Why is it necessary to use Fisher's z'?
8. What assumptions are made in the construction of a confidence interval on µ?
9. Under what circumstances would a researcher find it useful to construct a confidence interval?
10. Why is the construction of confidence intervals considered part of inferential statistics?
11. How does the t distribution compare with the normal distribution. How does the difference affect the size of confidence intervals constructed using z relative to those constructed using t? Does sample size make a difference?
12. Which would be more likely to be wider, a confidence interval on the mean based on a sample of 10 subjects or a confidence interval on the difference between means based on a sample of 10 subjects from each population? Assume that the variances in these populations are the same.
13. A population is known to be normally-distributed with a standard deviation of 2.8. Compute the 95% confidence interval on the mean based on the following sample of 6 numbers: 8, 9, 12, 13, 14, 16.
14. A person claims to be able to predict the outcome of flipping a coin. They are correct 12/18 times. Compute the 95% confidence interval on the proportion of times this person can predict coin flips correctly. What conclusion can you draw about this test of his ability to predict the future?
15. A hypothetical experiment is conducted to see whether cognitive therapy is more effective for relieving depression than is psychodynamic psychotherapy. Out of the population of depressed people in a certain area, 10 are sampled for the cognitive therapy group and 10 are sampled for the psychodynamic therapy group. After 6 weeks of therapy, the improvement in each patient is assessed. The improvement scores are shown below:
Cognitive Psychodynamic 9 3 7 2 7 4 8 0 3 5 8 2 7 4 5 3 6 2 8 5
Estimate the mean difference in effectiveness and compute a 95% confidence interval on this estimate. What conclusion about the relative effectiveness of the two treatments in the population.
16. An experiment compared the ability of 7 and 9 year olds to solve a problem requiring a certain type of abstract reasoning. Five of 21 seven-year olds and 14 of 16 nine-year olds solved the problem. Construct the 95% confidence interval on the difference in proportions.
17. In an experiment on the relationship between chess skill and memory for chess positions, one group of 18 chess players was presented with a meaningful chess position to memorize while another group of 20 chess players was given a random position to memorize. The correlation in the first group between each chess player's skill (as measured by his or her chess rating) and memory performance was .70; the correlation in the second group was only .11. Compute the 95% confidence interval on the difference in correlations.
18. An experiment is conducted comparing the effectiveness of two methods of teaching algebra. Ten gifted and 10 average students are taught using each method. There are therefore four groups of subjects. Their scores on a final exam are shown on the next card. Compute the 99% confidence interval on the difference between the mean of the students being taught by Method 1 and the mean of the students taught by Method 2. Hint: do this using a linear combination of means. Do not ignore the grouping based on ability.
Method 1 Method 2
Average Gifted Average Gifted 67 87 32 90 56 78 40 88 55 86 51 83 61 90 34 85 67 77 55 94 56 78 39 91 68 81 45 95 53 91 36 87