Question

Is smoking during pregnancy associated with premature births? To investigate this question, researchers selected a random sample of 138 pregnant women who were smokers. The average pregnancy length for this sample of smokers was 255 days. From a large body of research, it is known that length of human pregnancy has a standard deviation of 16 days. The researchers assume that smoking does not affect the variability in pregnancy length.

Find the 99% confidence interval to estimate the length of pregnancy for women who smoke.

(Note: The critical z-value to use, zc, is: 2.576)

Your answer should be rounded to 3 decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 255 days

Population standard deviation =    = 16 days

Sample size = n = 138

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

Margin of error = E = Z/2 * ( /n)

= 2.576 * ( 16 /  138 )

= 3.509

At 99% confidence interval estimate of the population mean is,

  ± E

255 ± 3.509   

( 251.491, 258.509 )