In Exercises, presume that the assumptions for regression inferences are met.Crown-Rump Length. Following are the data on age of fetuses and length of crown-rump from Exercise. x 10 10 13 13 18 19 19 23 25 28 y 66 66 108 106 161 166 177 228 235 280 a. Determine a point estimate for the mean crown-rump length of all 19-week-old fetuses.b. Find a 90% confidence interval for the mean crown-rump length of all 19-week-old fetuses.c. Find the predicted crown-rump length of a 19-week-old fetus.d. Determine a 90% prediction interval for the crown-rump length of a 19-week-old fetus.ExerciseApplying the Concepts and SkillsIn Exercises, we repeat the information from Exercises. For each exercise here, discuss what satisfying Assumptions 1–3 for regression inferences by the variables under consideration would mean.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
In Exercises, presume that the assumptions for regression inferences are met.
Crown-Rump Length. Following are the data on age of fetuses and length of crown-rump from Exercise.
| x | 10 | 10 | 13 | 13 | 18 | 19 | 19 | 23 | 25 | 28 |
| y | 66 | 66 | 108 | 106 | 161 | 166 | 177 | 228 | 235 | 280 |
a. Determine a point estimate for the mean crown-rump length of all 19-week-old fetuses.
b. Find a 90% confidence interval for the mean crown-rump length of all 19-week-old fetuses.
c. Find the predicted crown-rump length of a 19-week-old fetus.
d. Determine a 90% prediction interval for the crown-rump length of a 19-week-old fetus.
Exercise
Applying the Concepts and Skills
In Exercises, we repeat the information from Exercises. For each exercise here, discuss what satisfying Assumptions 1–3 for regression inferences by the variables under consideration would mean.
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