document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #820226 by Theo(13342) $\"\"$ $\"About$

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the mean of the population is 28.6
\n" ); document.write( "the sample size is 36.
\n" ); document.write( "the standard deviation of the population is 4.18.
\n" ); document.write( "the standard error is 4.18 / sqrt(36) = .6967 rounded to 4 decimal places.
\n" ); document.write( "critical z-score at two tailed alpha of .05 (.025 on each side) = plus or minus 1.96.
\n" ); document.write( "on the high side, 1.96 = (x - 28.6) / .6967.
\n" ); document.write( "solve for x to get x = 1.96 * .6967 + 28.6 = 29.966 rounded to 3 decimal places.
\n" ); document.write( "on the low side, -1.96 = (x - 28.6) / .6967.
\n" ); document.write( "solve for x to get x = -1.96 * .6967 + 28.6 = 27.234 rounded to 4 decimal places.
\n" ); document.write( "if the sample mean is between 26.966 and 27.234, you can assume that the population mean of 28.6 is good.
\n" ); document.write( "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.\r
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