Analyzing Birth Weight: T-Tests on Smoking Effects and Averages

Jose Lazo Stats Lab 5 Problem 1. The birthweight.csv dataset contains measurements on newborns as well as information about the parents of the newborns. The national average birth weight for newborns is 7.5 pounds. Perform a one-sample t-test at the =0.05 significance level to test if the average birth 𝛼 weight of newborns is different than 7.5 pounds. Create the corresponding confidence interval for the mean birth weight. Note: The t-test has an additional assumption–the data must be approximately normally distributed. So there is an extra step in our analysis. 1. State the hypotheses, define any parameters used. H o :u= 7.5 H 1 :u ≠ 7.5 u is the mean of the average birth weight of a newborn in pounds. 2. Check the conditions for performing the. ➔ We must assume that sample size of newborn weight were randomly selected ➔ We must assume that 7.5 pounds is less than or equal to 10% of the average birth weight of all babies. ➔ We must assume that 42 is less than 10% of worldwide newborns weight and that 42>30 ➔ Symmetrical distribution. Normal check is most likely met.

3. Calculate and report the test statistic. One Sample T-Test One Sample T-Test t df p Birthweight 35.404 41 <.001 Note. For the Student t-test, the alternative hypothesis specifies that the mean is different from 0. Note. Student's t-test. 4. Conclude in the context of the problem. With a p-value at .001, there is not enough evidence to suggest that the national birth weight of babies is different than 7.5 pounds. 5.Create a confidence interval for the mean birth weight of newborns. (Found in Descriptives) -(6.850lbs-7.679lbs) -95% CI that the mean of the birthweight is between the numbers above. Independent Samples T-Test Independent Samples T-Test 95% CI for Mean Difference t df p Mean Difference SE Difference Lower Upper Birthweig ht - 5.43 6 4 0 <Â .0 01 -2.447 0.450 -3.357 -1.537 Note. Â Student's t-test.

Problem 2 There are concerns that smoking adversely affects newborns in a variety of ways, in particular the birth weight of the child. Using birthweight.csv, perform a two-sample t-test at the =0. 05 𝛼 significance level to see if there is a difference in the mean birthweight of newborns whose mother smoked and those whose mother did not smoke during pregnancy. 1.State the hypotheses, define any parameters used. H o :u nx - u x =0 H 2 :u nx - u x ≠ 0 ❖ u is the average smoker and nonsmoker mothers of the newborn babies. 2.Check the conditions for performing the test. ➔ We must assume that the sample of mothers used in the smoking and nonsmoking sample was selected at random ➔ We also assume that 42 is less than 10% of worldwide mothers who smoke and those who don’t 42 > 30. ➔ The data appears to be skewed to the right. ➔ 0= nonsmokers, 1= smokers. 3.Calculate and report the test statistic. Independent Samples T-Test Independent Samples T-Test t df p

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Birthweight 2.054 40 0.047 Note. Â Student's t-test. 4.Conclude in the context of the problem. With our P-value at 0.047, there is enough evidence to suggest that there is a difference between mean weight of newborn and whose mothers have smoked and have not smoked during pregnancy. 5.Create a confidence interval for the mean difference in birth weights of newborns between mothers who smoke and those who did not smoke. (Found in T-test) (0.013 lbs - 1.162lbs ) There is a 95% CI that the newborn's birth weight mean are between the numbers stated above. Independent Samples T-Test Independent Samples T-Test 95% CI for Mean Difference t df p Mean Difference SE Difference Lower Upper Birthweig ht 2.0 54 4 0 0.0 47 0.813 0.396 0.013 1.612 Note. Â Student's t-test.

Stats Lab 5

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