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
Algebra ->
Statistics
-> Hypothesis-testing
-> 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
Log On
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):
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.
