Question

Is smoking during pregnancy associated with premature births? To investigate this question, researchers selected a random sample of 111 pregnant women who were smokers. The average pregnancy length for this sample of smokers was 262 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, $z_c$, is: 2.576) ( , ) Your answer should be rounded to 3 decimal places.

Answer 1

Solution :

Given that,

= 262

= 16

n = 111

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576 * (16 / 111)

= 3.912

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

- E < < + E

262 - 3.912 < < 262 + 3.912

258.088 < < 265.912

(258.088 , 265.912)