ASK YOUR TEACHER PRACTICE ANOTHER T. '[I0.27 Points] BBUNDERSTAT12 7.4.019. The U.5. Geologlail Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987, Let x1 be a random variable that represents the time Interval (In minutes) between old Faithful emotions for the years 1948 to 1952. Based on 9740 observations, the sample mean Interval was Tr! = 62.2 Faithful emotions for the years 1983 to 1987. Based on 23,351 observations, the sample mean time Interval was E2 the population mean of x' and let p2 be the population mean of x2. minutes. Let x2 be a random variable that represents the time interval In minutes between Old = 72.0 minutes. Historical data suggest that 51 - 8.00 minutes and a2 = 12.13 minutes. Let \"1 be (a) Compute a 95% condence interval for pl - "Z. (Use 2 decimal places.) lower limit upper limit (b) Comment on the meaning of the condence interval in the context of this problem. Does the Interval consist of positive numbers only? negative numbers only? a mix ol' positive and negative numbers? Does It appear (at the 95% condence 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 condence Interval. ~ Because the Interval contains only negative numbers, we can say that the interval length between eruptions has gotten longer. Need Help? m a. [-10.27 Points! BBUNDERSTAT12 7.4.020.Ml. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER I A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let x1 be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let)!2 be the empathy score of a father. A random sample of 36 mothers gave a sample mean of :71 = 59.35. Another random sample of 32 fathers gave 7:2 = 60.06. Assume that .71 =1 11.13 and a: = 11.04. (a) Let H be the population mean of X1 and let 142 be the population mean of x2, Find a 99% confidence interval for M i \"2. (Round your answers to two decimal places.) i lower limit l l upper limit (o) Examine the condence interval and explain what it means in the context of this problem. Does the condence interval contain all positive, l all negative, or both positive and negative numbers? What does this tell i you about the relationship between average empathy scores for mothers compared with those for fathers at the 99% condence level? l, Because the interval mntalns only positive numbers, we can say that the mothers have a higher mean empathy score. Because the interval contains both positive and negative numbers, we can not say that the mothers have a higher mean empathy score. We can not make any conclusions using this condence interval. ' Because the interval contains only negative numbers, we can say that the fathers have a higher mean empathy score. . Need Help? . \\
