Crawling data collected by child development scientists pro- duced this confidence interval for the average age (in weeks) at which babies begin to crawl: t-interval for m 30.65 6 m(age) 6 32.89 (95.00% confidence): a) explain carefully what the software output means. b) what is the margin of error for this interval

a) We can be 95% sure that true average age (in weeks) at which babies begin to crawl is between 30.65 weeks and 32.89 weeks.

b) Margin of error for the confidence interval is 1.12 weeks.

Step-by-step explanation:

Let m be the estimate of the average age (in weeks) at which babies begin to crawl

Let ME be the margin of error.

then the difference between the upper bound and the lower bound gives:

m+ME - (m-ME) = 2ME = 32.89-30.65=2.24 which gives

ME=1.12 weeks

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: