SOLUTION: A sociologist wishes to see if it is true that for a certain group of professional women, the average age at which they have their first child is 28.6 years. A random sample of 3

Question 1188836: A sociologist wishes to see if it is true that for a certain group of professional women, the average age at which they have their first child is 28.6 years. A random sample of 36 women is selected, and their ages at the birth of their first child are recorded. At α = 0.05, does the evidence refute the sociologist’s assertion? Assume σ = 4.18
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the mean of the population is 28.6
the sample size is 36.
the standard deviation of the population is 4.18.
the standard error is 4.18 / sqrt(36) = .6967 rounded to 4 decimal places.
critical z-score at two tailed alpha of .05 (.025 on each side) = plus or minus 1.96.
on the high side, 1.96 = (x - 28.6) / .6967.
solve for x to get x = 1.96 * .6967 + 28.6 = 29.966 rounded to 3 decimal places.
on the low side, -1.96 = (x - 28.6) / .6967.
solve for x to get x = -1.96 * .6967 + 28.6 = 27.234 rounded to 4 decimal places.
if the sample mean is between 26.966 and 27.234, you can assume that the population mean of 28.6 is good.
otherwise, you can assume that it is not good and that the sample mean is more likely to be closer to the real population mean.

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