11. [-/4.42 Points] DETAILS BBUNDERSTAT12 7.4.017.S. MY NOTES ASK YOUR TEACHER A random sample of 362 married couples found that 296 had two or more personality preferences in common. In another random sample of 576 married couples, it was found that only 20 had no preferences in common. Let p, be the population proportion of all married couples who have two or more personality preferences in common. Let p2 be the population proportion of all married couples who have no personality preferences in common. LA USE SALT (a) Find a 95% confidence interval for P1 - P2. (Use 3 decimal places.) lower limit upper limit (b) Explain the meaning of the confidence interval in part (a) in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you (at the 95% confidence level) about the proportion of married couples with two or more personality preferences in common compared with the proportion of married couples sharing no personality preferences in common? We can not make any conclusions using this confidence interval. Because the interval contains both positive and negative numbers, we can not say that a higher proportion of married couples have two or more personality preferences in common. Because the interval contains only positive numbers, we can say that a higher proportion of married couples have two or more personality preferences in common. Because the interval contains only negative numbers, we can say that a higher proportion of married couples have no personality preferences in common. 12. [-/4.51 Points] DETAILS BBUNDERSTAT12 7.4.019. MY NOTES ASK YOUR TEACHER The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x] be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9600 observations, the sample mean interval was x, = 61.6 minutes. Let x2 be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 24,404 observations, the sample mean time interval was x2 = 70.8 minutes. Historical data suggest that oj = 8.35 minutes and 62 = 12.48 minutes. Let /1 be the population mean of x1 and let #2 be the population mean of x2- (a) Compute a 99% confidence interval for #1 - 2. (Use 2 decimal places.) lower limit upper limit (b) Comment on the meaning of the confidence interval in the context of this problem. Does the interval consist of positive numbers only? negative numbers only? a mix of positive and negative numbers? Does it appear (at the 99% confidence level) that a change in the interval length between eruptions has occurred? Many geologic experts believe that the distribution of eruption times of Old Faithful changed after the major earthquake that occurred in 1959. Because the interval contains only positive numbers, we can say that the interval length between eruptions has gotten shorter. Because the interval contains both positive and negative numbers, we can not say that the interval length between eruptions has gotten longer. We can not make any conclusions using this confidence interval. Because the interval contains only negative numbers, we can say that the interval length between eruptions has gotten longer
