Question

Is smoking during pregnancy associated with premature births? To investigate this question, researchers selected a random sample of 128 pregnant women who were smokers. The average pregnancy length for this sample of smokers was 265 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 90% confidence interval to estimate the length of pregnancy for women who smoke. (Note: The critical z -value to use, z c , is: 1.645) ( , ) Your answer should be rounded to 3 decimal places.

Answer 1

Answer:(262.674,267.326)

Explanation:

265-2.326=262.674

265+2.326=267.326

Answer 2

Confidence interval is 128±2.326 days (between 125.674 days and 130.326 days) in 90% confidence level

Step-by-step explanation:

Confidence interval can be calculated as M±ME where

• M is the average pregnancy days of smoking women and
• ME is the margin of error in 90% confidence level.

Margin of Error in 90% confidence level can be calculated using the formula:

ME=
`(z*s)/(√(N) )` where

• z is the z-value in 90% confidence level (1.645)
• s is the standard deviation of pregnancy length (16)
• N is the sample size (128)

putting these numbers in the formula, we get:

ME=
`(1.645*16)/(√(128) )` =2.326

then confidence interval is 128±2.326 ( between 125.674 and 130.326 ) in 90% confidence level