SOLUTION: Please help me solve this: It has been known in the past that the average number of children of a Filipino family is 6. A random sample of 25 families were selected and found

Question 1174739: Please help me solve this:
It has been known in the past that the average number of children of
a Filipino family is 6. A random sample of 25 families were selected and
found to have an average of 3 children with a standard deviation of 1
child. Can we say that the number of children of a Filipino family has
gone lower?
Thank you!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
it sure sounds like it.

let's see what the statistical analysis says.

sample size is 25
average is 3 children per family.
standard deviation is 1 child.

since the standard deviation is from the sample rather than the population, then the t-score analysis is considered.

the standard error is equal to the sample standard deviation divided by the square root of the sample size.

that makes the standard error equal to 1/sqrt(25) = 1/5 = .2.

the t-score is equal to (x - m) / s

x is the raw score from the sample
m is the assumed mean from the population.
s is the standard error.

the standard error is the standard deviation of the distribution of sample means.

the t-score is equal to (3 - 6) / .2 = -3/.2 = -15.

at two-tailed 99% confidence interval, the critical t-score with 24 degrees of freedom (sample size minus 1 = degrees of freedom) would be plus or minus 2.797.

a t-score of -15 with 24 degrees of freedom is well beyond the left side critical t-score of-2.797 with 24 degrees of freedom.

it appears that there is overwhelming evidence that the average number of children in a filipino family has gone lower.

it's pretty safe to say that it has.

here's the critical t-score table that i used.

https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf

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