Question 4

4) Consider the results of 3(b). Notice that all the data fit within the 99% confidence interval. Is this usually the case (in other words, will a 99% CI contain most of the observations)? Caution: a lot of people get this wrong! Here's a hint: suppose you had measured the worms in 6000 acres (instead of just 7). What happens to the confidence interval? If you're not sure, substitute 6,000 for 7 in your calculation for 3(b) to see what happens. 5) Suppose the (sample) average height of women in the U.S. is y = 161.8cm, and the average height of men in the U.S. is y = 175.4cm. For both the sample standard deviation is about s = 7.62cm. (a) Suppose you take a sample of 7 women and 7 men. Construct a 95% CI for both. Do the confidence intervals overlap? (b) Now repeat using a sample of 175 women and 200 men. Do the confidence intervals overlap? (c) Can you explain what happened? Why is sample size important if you're trying to find differences between groups? (Statistical comment: comparing CI's is not the correct way of comparing two groups, but it can give you an idea if there's a difference). 6) Use the data for heights that you collected in recitation last week and construct a 90% CI. Use R to do this. While your lecture may not have learned about the t-test yet, a CI is just the reverse of a one sample t-test. To get Confidence Intervals in R see the following page