5. In a small pilot study of the effe were obtained for the birth weights of 30

Question

5. In a small pilot study of the effe were obtained for the birth weights of 30 children born to cocaine users: x-2715 g, s = the sample data be assumed to be approximately Normally distributed, (a) yes or no? (b) Why or why not? Test the claim that babie 3103 g, the birth weight of babies born to non-users of cocaine. (State (c) claim, (d) (e) null and (f) alternative hypotheses, (g) test statistic used, equivalent and (i) Singer et al., J Amer Med Assocation, 291 (20) cts of pre-natal cocaine use on infants, the following sample data 645 g. Can s born to cocaine users have a mean birthweight that is less than counter-claim, (h) its numerical value, (i) its P your conclusion in language that a neonate's parent would understand). After 10 6. Heights, in inches, of 15 year old American boys are distributed as N(65.o, 2.4). What sample size would you need if you wanted to confirm that mean height is indeed 65.0 inches with a margin of error of ± 0.5 inches and a confidence level of 95%? Assume, further, that you wished to interview a sample of these boys about a new bicycle design. If you had no prior idea what proportion would be interested, how large a sample would you need to ensure that your estimated proportion was accurate to within ± 5% with a confidence level of 90%? If, after some limited preliminary sampling, you find that about 14% of 15 year old boys are keen cyclists, how large a sample would you then require, given the same margin of error and confidence level requirements? 3

Explanation / Answer

Solution to question 6

Margin of Error = Z value * Standard error

1) Margin of error = +-0.5 = +-z0.025*(Standard deviation/n0.5)

= 0.5 = 1.96*(2.4/n)0.5

So, n = 36.88 = 37

2) Margin of error = +-5%

5% = 1.6449*((0.5)(0.5)/n)0.5 (assumed proportion to be 50%)

n = 271

3) 5% = 1.6449*((0.14)(0.86)/n)0.5

n = 130

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