# 2. A small study (n-10) is designed to assess if there is an association between smoking in pregnancy and low birth weight. Low birth weight babies are those born less t 5.5 pounds. The following data represent the birth weights, in pounds, of babies born to mothers who reported smoking in pregnancy and those who did not. han Mother smoked in pregnancy Mother did not smoke during pregnancy 5.1 5.0 4.2 4.8 3.3 3.9 5.3 4.9 5.4 4.6 Is there a significant difference in birth weights between mother who smoked during pregnancy and those who did not? Apply the Mann Whitney U Test at a 5% level of significance Complete the table below. Ranks Total Sample (Ordered Smallest to Largest) Mother oked Di Not Smoked Did Not Smoke Smoke Smoked in Did Not Pregnancy Smoke inn Pregnancy k 4.9 5.4 3.3 5.0 4.2 4.8 3.3 3.9 2 4.6 ー 4.6 4.9 5.2 2. cont. ntlh ,- 515)+5 (G 22

Question

Please let me know if there is a significant evidence to show that the populations are not equal. Thank you.

Step 1

Mann-Whitney U Test:

Mann-Whitney U test is a non-parametric test used to check for differences between two sets of observations, usually based on samples taken from two separate populations.

In this procedure, the sample observations from the two populations are first combined and given a combined rank.

Suppose the number of observations in sample 1 is n1 and the number of observations in sample 2 is n2.

Let R1 be the sum of ranks of the sample 1 observations and R2 be the sum of ranks of the sample 2 observations.

Then, the Mann-Whitney U test statistic is the smaller of U1 and U2, defined as follows:

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