I was making an attempt to solve the following problem sets, however, my answer 15.913 seemed quite different from that in the answer key 16.84. I have checked my answer a few times and re-doing the question as well, but I was consistently pulled back to the same outcome of 15.913. Appreciate some guidance and advice please.
Question
A recent study of home technologies reported the number of hours (to the nearest hour) of personal computer usage per week for a sample of 10 persons. Excluded from the study were people who worked out of their home and used the computer as a part of their work.
8, 5, 6, 8, 6, 1, 5, 6, 9, 4
In a study with sample size of 30 people who worked out of their home and used the computer as a part of their work, the sample mean and standard deviation of the number of hours personal computer usage per week are 42.0 and 6.4, respectively. If we wants to combine the results of these two samples, find the standard deviation of the number of hours personal computer usage per week of in the combined sample.
My Attempt
New Sample
n=10, sample mean = 5.8, Sum(xi) = 58, Sum(xi^2) = 384
Old Sample
n=30, sample mean = 42, s= 6.4, Sum(xi) = (30)(40) = 1260, Sum(xi^2) = (30)(40^2) = 52920
Combined Sample
n=40
sample mean = (1260+58)/40 = 32.95
Sum(xi) = 1260 + 58 = 1318
Sum(xi^2) = 384 + 52920 = 53304
s = SqRt{[53304 - (40)(32.95^2)]/[40-1]} = 15.91314
The answer offered in the answer key 16.84 seemed quite different from my 15.91314. Appreciate any advice if there might be some steps which I may be doing wrongly.