8. In a study of the relationship between birth order and college success, an investigator found that 140 in a sample of 200 college graduates were rstborn or only child. In a sample of 120 non- graduates of comparable age and socioeconomic background, the number of rstborn or only Chlld was 66. Estimate the difference between the proportions of rstborn or only child in the two populations from which these samples were drawn using a 90% condence interval and interpret your results. 9. The mean weight of an ordinary key is an important consideration, as most people carry a pockeiful of keys. A manufacturer claims that a new process produces a lighter and more durable key. Independent samples of both types of keys were obtained, and each key was carefully weighed and its weight (in ounces) was recorded. The resulting summary statistics are given in the following table. Sample size Sample mean Sample Variance Old Process 10 0.0137 New Process 10 0.0202 Assume that the underlying distributions are normal and the population variances are equal. (a) Construct a 99% confidence interval for the difference between the mean weight of a new- process key and the mean Weight of an old-process key. (b) Can you be 99% condent that the mean weight of a new-process key is less than the mean weight of an old-process key