Chapter 10, Problem 15

In Norway, the distribution of birth weights for full-term infants whose gestational age is 40 weeks is approximately normal with mean = 3500 grams and standard deviation = 430 grams. An investigator plans to conduct a study to determine whether the birth weights of full-term babies whose mothers smoked throughout pregnancy have the same mean. If the true mean birth weight for the infants who smoked is as low as 3200 grams (or as high as 3800 grams), the investigator wants to risk only a 10% chance of failing to detect this difference. A two-sided test conducted at the 0.05 level of significance will be used. What sample size is needed for this study? There is a trick in this question!! note that 3200 and 3800 are equally distant from 3500, so think two-sided!

References:

1) Z-tables: http://www.z-table.com/

2) Percentiles of t distribution link:

http://personal.psu.edu/acq/401/tables/t.pdf

According to my book,

df = 0.10 = 90% (link)

df = 0.05 = 95% (link)

df = 0.025 = 97.5% (link)

df= 0.01 = 99% (link)

df = 0.005 = 99.5% (link)

df = 0.0005 = 99.9% (link)