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Unformatted text preview: Exam 1 Review Example 1: Do pregnant women who smoke have babies with lower birth weight than those who do not smoke? A researcher thinks so. To test her conjecture she has recorded the birth weight of babies born at Shands in a given period, together with the smoking status of the mother and summarized the data as shown below: Smoking Status Sample sizes (n i ) Sample Statistics Sample Means ( i X ) Sample Standard Deviations (S i ) 1. Smokers 134 2733 grams 599 grams 2. Nonsmokers 5974 3118 grams 672 grams Do the above data support the conjecture of the researcher? 1. What type of a problem is this? No. of populations : 2 Population 1 : Set of ALL pregnant women who smoke. Population 2 : Set of all pregnant women who do not smoke. Exam 1 Review, Spring 2008 Page 1 of 21 Samples : We have 2 independent samples, one from each population. No. of Parameters : 2 1 ST parameter : µ 1 = µ S = mean birth weight of babies born to ALL pregnant women who smoke and 2 nd parameter : µ 2 = µ N = mean birth weight of babies born to ALL pregnant women who do not smoke Parameter of interest : µ 1  µ 2 Type of response variable : Quantitative. Why? Because birth weight takes only numerical values . Are the samples dependent or independent ? Ans : Independent. Why? Because smokers and nonsmokers correspond to different women. Hence, what type of problem do we have? Ans : Comparing 2 population means using two independent random samples . Exam 1 Review, Spring 2008 Page 2 of 21 2. What are hypotheses to be tested? Ho: µ 1  µ 2 = 0 vs. Ha: µ 1  µ 2 < 0 How can you tell? Since the researcher guesses that smokers give birth to babies having lower birth weight than do non smokers. 3. What is the test statistic for this problem? Since we have quantitative data, (and the population variance is unknown) the test statistic to use is 1 2 (133) 2 2 1 2 1 2 ( ) 0 ~ X X T t S S n n = + where 1 2 X X is an estimate of µ 1  µ 2 and 2 2 1 2 1 2 S S n n + is the estimate of the standard error of 1 2 X X . Finally, since the two sample sizes are very different we will use df = smaller of {(n 1 – 1) and (n 2 – 1)} = 133 for the test statistic. Exam 1 Review, Spring 2008 Page 3 of 21 Since the df is too large, we will use the normal distribution. (Why?) Ans : Since the t distribution approximates the normal distribution for large sample sizes. 5 . Are all the assumptions needed for this procedure satisfied? a) Random and independent samples which we think have been satisfied since the samples were randomly selected and were also independent since the smokers and non smokers correspond todifferentwomen. . b) The type of random variable (birth weight) is Quantitative. So this assumption is satisfied....
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 Spring '08
 Fasig
 Normal Distribution, Standard Deviation, birth weight

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