Question

Is smoking during pregnancy associated with premature births? To investigate this question, researchers selected a random sample of 148 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 95% confidence interval to estimate the length of pregnancy for women who smoke.

(Note: The critical z-value to use, zc, is: 1.960)

( , )

Your answer should be rounded to 3 decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 262

Population standard deviation =    = 16

Sample size = n =148

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.960 * ( 16 /  148 )

= 2.578
At 95% confidence interval estimate of the population mean
is,

- E < < + E

262 - 2.578 <   < 262 + 2.578

259.422<   < 264.578

( 259.422 ,  264.578, )