Measuring the moon\'s orbit. Refer to the American Journal of Physics (Apr. 2014
ID: 3181264 • Letter: M
Question
Measuring the moon's orbit. Refer to the American Journal of Physics (Apr. 2014) study of the moon's orbit. Exercise 11.23 (p. 598). Recall that the angular size (y) of the moon was modeled as a straight-line function of height above horizon (x). A MINITAB printout showing both a 95% prediction interval for y and a 95% confidence interval for E(y) when x = 50 degrees is displayed below. a. Give a practical interpretation of the 95% prediction interval. b. Give a practical interpretation of the 95% confidence interval. c. A researcher wants to predict the angular size of the moon when the height above the horizon is 80 degrees. Do you recommend that the researcher use the least squares line shown in the printout to make the prediction? Explain.Explanation / Answer
a) n statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval in which future observations will fall, with a certain probability, given what has already been observed.
The prediction interval is between 323.502 and 326.108.
b)
If repeated samples were taken and the 95% confidence interval was computed for each sample, 95% of the intervals would contain the population mean. A 95%confidence interval has a 0.95 probability of containing the population mean. 95% of the population distribution is contained in the confidence interval.
Based on our sample data, we are 95% confident that the "true" average angular size is between 324.448 and 325.163. Another interpretation:It is believe that the population mean(average angular size) lies between these two bounds of 324.448 and 325.163 since 95% of the time confidence intervals contain the true mean.
c)
Angular size Y = 321 + 0.0384 Horizon
Given Horizon = 80
The predict value of angular size is
Y = 321 + 0.0384 (80) = 324.072