Are the two estimated birth weights significantly different practically and statistically? Please briefly explain.
Promoting population growth is an important policy of an anonymous country, and an equally important issue is to improve its people's health, both physically and spiritually. In relation to this, a problem of considerable interest to the country's health officials as well as to its ordinary people is to understand the effects of smoking during pregnancy on infant health. One typical and convenient measure of infant health is birth weight since a new-born infant who is too light can put the infant at risk for contracting various illnesses. Hence a simple linear regression (SLR) model could be proposed as follows: \[ \text { weight }=\beta_{0}+\beta_{1} \text { ciga }+e, \] (1p) where weight is birth weight in ounces and ciga is average number of cigarettes the mother smoked per day during pregnancy. Using the popular ordinary least squares (OLS) method and the relevant data from BabyWeight - a dataset on some relevant variables or factors compiled from a recently-conducted random survey on 483 women who gave birth to a little baby in the past three months in an Eastern city of the country, Model (1p) is estimated as follows: \[ \begin{aligned} \text { weight }= & 121.3584-0.6612 \text { ciga }+\hat{e}, \\ & (1.0388) \quad(0.1176) \\ & {\left[n=483, R^{2}=0.0617, S S R=189,594.0898\right] } \end{aligned} \] Q1 (12 marks): For a typical non-smoking woman A and a typical smoking woman B who smoked 10 cigarettes per day during pregnancy, find the estimated or expected birth weights (denoted as weight A1andlightB1) of their new-born babies based on Model (1s). Are the two estimated birth weights significantly different practically and statistically? Please briefly explain.
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