23.26 Using the Internet. Return to the study in Exercise 22.20 (page 541), which found that 168 of an SRS of 200 entering students at a large state university said that they used the Internet frequently for research or homework. This differed significantly (P = 0.242) from the 81.8% of all first-year students in the country who claim this.

  1. (a) It may be more informative to give a 95% confidence interval for the proportion of this university’s entering students who claim to use the Internet frequently for research or homework. Do this.

  2. (b) Is the 81.8% national figure included in your confidence interval? Explain why you are or are not surprised by this.

  3. (c) Suppose that 1680 of an SRS of 2000 entering students at a large state university had said that they used Internet frequently for research or homework. In this situation, the results would differ significantly (P < 0.001) from the 81.8% of all first-year students in the country who claim this. Why are these results statistically significant when the sample proportion is the same as that in the original sample (1680/2000 = 168/200 = 0.84)?