True or False questions.

1. If you test H0: ₁-₂=0 using =.05, and the two-sided p-value is .02, then the two population means are statistically significantly different.
2. The width of a confidence interval will decrease if either the population variance decreases (all other things being held constant) or the sample size increases (all other things being held constant)
3. For any measure that is normally distributed, approximately 95% of observations will be within 2 standard deviations of the mean.
4. The p-value from a two-tailed test is always larger than the p-value from a one-tailed test
5. If your null hypothesis is that the difference between two means is 5, then the t-statistic for the test is if you do not want to assume that the variances are the same in the two groups.
6. If the 95% confidence interval around a sample mean is (2, 77), then you are 95% confident that the sample mean is between 2 and 77.
7. If the p-value is .90, you are 90% confident the two groups are the same.
8. If a study is not randomized, you will still get unbiased estimates of a treatment effect as long as your sample size is large enough.
9. If two events A and B are mutually exclusive and do not have probability 0, then they cannot be independent.