The table below shows the birth weights of three groups of infants classified by the mother's smoking status based on the number of packs of cigarettes she consumes in a day. Determine whether there is a significant difference among the three groups of weights at the 5% level: Table Z: Infant Birth Weights According to the Smoking Status of the Mother Number of packs of cigarettes per day None 1 pack More than 1 Birth wt (kg) 405 374 2.71 3.23 275 261 3.94 284 2.52 3.86 3.44 36 3.88 3.83 318 3.23 3.88 22 3.59 3.42 1.82 318 3.51 3.45 3.42 2.88 2.79 3.51 3.05 3.26 Patterned from Bohnenblust and Kuzma (2015)
Added by Jennifer M.
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We can do this using Excel or a calculator. Here are the results: - None: mean = 3.23 kg - 1 pack: mean = 3.44 kg - More than 1 pack: mean = 3.05 kg Show more…
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In a study of the impact of smoking on birth weight, researchers analyze birth weights (in grams) for babies born to 189 women who gave birth in 1989 at a hospital in Massachusetts. In the group, 74 of the women were categorized as "smokers" and 115 as "nonsmokers." The difference in the two sample mean birth weights (nonsmokers minus smokers) is 281.7 grams and the 95% confidence interval is (76.5, 486.9) Which gives the best interpretation of what we can conclude about the impact of smoking on birth weight? A. This study does not suggest that there is a difference in mean birth weights when we compare smokers to nonsmokers. B. We are 95% confident that on average, smoking causes lower birth weights of between 76.5 grams to 486.9 grams. C. There is a 95% chance that if a woman smokes during pregnancy her baby will weigh between 76.5 grams to 486.9 grams less than if she did not smoke. D. When smokers are compared to nonsmokers, we are 95% confident that the mean weight of babies of nonsmokers is between 76.5 grams to 486.9 grams more than the mean weight of babies of smokers.
Sri K.
Birthweight 4.55 4.32 4.1 4.07 3.94 3.93 3.77 3.65 3.63 3.42 3.35 3.27 3.23 3.2 3.15 3.11 3.03 2.92 2.9 2.65 3.64 3.14 2.78 2.51 2.37 2.05 1.92 4.57 3.59 3.32 3 3.32 2.74 3.87 3.86 3.55 3.53 3.41 3.18 3.19 2.66 2.75 smoker (no=0, yes=1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Show your work for the calculations. State the result of testing the null hypothesis. State if the hypothesis is supported or not. In 1 to 3 paragraphs, explain the results of the test. Using the difference of means test the following: Hypothesis: The mean birth weight of babies born to mothers who do not smoke is higher than the mean birth weight of babies born to mothers who do smoke. Null hypothesis: The mean birth weight of babies born to mothers who do not smoke is not higher than the mean birth weight of babies born to mothers who smoke. (assume data in the data set is a sample)
Ana Carolina D.
The birth weights (in grams) are given for babies born to 22 mothers who smoked during their pregnancy and to 35 mothers who didn't smoke during their pregnancy. For your reference, 3200 grams is about 7 pounds. Non-Smoking Group: 3612 3640 3444 3388 3612 3080 3612 3080 3388 4368 3612 3024 2436 4788 3500 4256 3640 4256 4312 4760 2940 4060 4172 2968 2688 4200 3920 2576 2744 3864 2912 3668 3640 3864 3556 Smoking Group: 3276 1974 2996 2968 2968 5264 3668 3696 3556 2912 2296 1008 896 2800 2688 3976 2688 2002 3108 2030 3304 2912 For the non-smoking group, do the following: 1) Construct a 95% confidence interval for the average weight of a baby born to a non-smoking mother. 2) Now suppose a researcher wants to estimate the average weight of a baby born to a non-smoking mother within 50 grams. How large a sample would be required to do so? Use σ = 600 grams for your calculations. For the smoking group, do the following: 3) Construct a 95% confidence interval for the average weight of a baby born to a smoking mother. 4) Now suppose a researcher wants to estimate the average weight of a baby born to a smoking mother within 50 grams. How large a sample would be required to do so? Use σ = 800 grams for your calculations. Compare your results: 5) A researcher thinks that it is possible that the average weight of a baby born to a non-smoking mother is equal to the weight of a baby born to a smoking mother. Based on your confidence intervals, what would you say to the researcher? (Note: I am telling you to use your confidence intervals since we do not cover the hypothesis test for this in this course). Test a claim: 6) A researcher also claims that the standard deviation of weights of babies born to smoking mothers is no more than 800. Test this claim using α = 0.05. Interpret this result using non-statistics language.
Jay P.
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