Please help Millis and Seng (1954) reported results from a study on the relation
ID: 3255087 • Letter: P
Question
Please help
Millis and Seng (1954) reported results from a study on the relation of birth order to the birth weight of human infants. The table below records frequency distributions they obtained of the birth weights of all first-born and eighth-born male infants of Chinese patients at the Kandang Kerbau Maternity Hospital in Singapore in 1950 and 1951: In other words, there were 1, 932 first-born male infants in the overall sample, of whom 2 had birth weights between 3 pounds 8 ounces and 3 pounds 15 ounces, and there were 307 eighth-born male infants in the sample, of whom 1 weighed between 10 pounds 0 ounces and 10 pounds 7 ounces (and so on). By placing all of the infants in each frequency category at the center of the category (which is not quite right, but it will do for our purposes here), Ive worked out that the mean and SD of the birth weights of the first-born infants (expressed in ounces) were approximately 106.1 and 12.2, respectively, and the corresponding values for the eighth-born infants were 114.7 and 15.0. (a) Does this difference seem large to you in practical terms? (In addition to making our usual percentage difference calculation, you could, for example, consider this situation from the point of view of the mothers who gave birth to these babies.) Explain briefly. (b) Set up a statistical model for this situation, being explicit about the population, sample and imaginary data sets, and use your model (including the usual inferential summary) to build a 95% confidence interval for the population mean difference in birth weight (what is the population here, precisely?). Is this difference large in statistical terms? Explain briefly.Explanation / Answer
a. Mean of first born infants = 106.1
Mean of eighth born infants = 114.7
Percentage difference = (114.7-106.1)/106.1*100 = 8.105%
From the point of view of the mother it can be seen that the difference is large and they have to carry a heavire baby in their womb.
b.
For mean difference in baby weight, diff = mean_first born - mean_eighth born
We need to check if diff = 0 or not.
H0: diff = 0
Ha: diff not equal to 0
The population here is the entire dataset and the sample is a any random sample from the population
95%CI for difference in means: diff - Z0.975*SD, diff + Z0.975*SD
diff = 114.7-106.1 = 8.6 ounce
SD = sqrt(first_bornSD^2 / n1 + eighthborn_SD^2/n2) = sqrt(12.2^2/1932 + 15^2/307) = 0.899 ounce
95% CI = 8.6-1.96*0.899, 8.6+1.96*0.899 = 6.838, 10.362
As 0 doe not lie in the confidence interval, the difference is large in statistical terms